Big Data: Big Data merujuk pada volume besar dan kompleks data yang tidak dapat secara efektif diolah atau dikelola menggunakan metode tradisional pemrosesan data. Data dalam skala besar ini seringkali berasal dari berbagai sumber, termasuk transaksi bisnis, media sosial, sensor IoT (Internet of Things), rekaman log, dan data lainnya. Big Data memiliki tiga karakteristik utama yang dikenal sebagai 3V: Volume (volume besar data), Variety (keragaman jenis data), dan Velocity (kecepatan pengumpulan dan pemrosesan data).
Tren Big Data di Masa Depan:
Peningkatan Penggunaan Kecerdasan Buatan (AI) dan Machine Learning (ML): Di masa depan, AI dan ML akan semakin mendominasi pengolahan dan analisis Big Data. Ini akan memungkinkan sistem untuk secara otomatis mengidentifikasi pola, tren, dan wawasan yang lebih dalam dari data berskala besar.
Integrasi Big Data dengan Internet of Things (IoT): Seiring dengan pertumbuhan IoT, akan ada integrasi yang lebih erat antara Big Data dan data yang dihasilkan oleh perangkat IoT. Ini akan memberikan pemahaman yang lebih baik tentang kinerja perangkat, pemantauan real-time, dan mendukung pengambilan keputusan yang lebih tepat waktu.
Keamanan dan Kepatuhan:
Edge Computing untuk Pengolahan Data di Tempat: Seiring dengan peningkatan jumlah data yang dihasilkan oleh perangkat di edge devices, pengolahan data di tempat (edge computing) akan menjadi tren, mengurangi latensi dan memungkinkan pengambilan keputusan yang lebih cepat.
Penggunaan Quantum Computing: Meskipun masih dalam tahap pengembangan, quantum computing memiliki potensi untuk mengubah paradigma dalam pengolahan data berskala besar dengan memecahkan masalah yang sulit atau bahkan tidak dapat dipecahkan oleh komputer klasik.
Pengembangan Infrastruktur Big Data yang Lebih Efisien: Dengan meningkatnya kesadaran akan dampak lingkungan, akan ada peningkatan fokus pada pengembangan infrastruktur Big Data yang lebih efisien secara energi untuk mengurangi jejak karbon.
Tren-tren ini mencerminkan evolusi Big Data sebagai disiplin yang terus berkembang, memanfaatkan teknologi baru untuk memberikan wawasan yang lebih dalam dan memberdayakan organisasi untuk membuat keputusan yang lebih cerdas dan cepat.
Salah satu bentuk data yang termasuk ke dalam big data adalah Data Time Series
Data Time Series adalah data yang diperoleh dari pengamatan satu objek dari beberapa periode waktu. Misalnya data jumlah mahasiswa dari tahun ke tahun, data nilai tukar dolar terhadap rupiah dari hari ke hari, data kasus covid dari bulan januari 2020 sampai periode saat ini, dan masih banyak contoh yang lainnya.
Time series analysis adalah teknik statistik yang digunakan untuk menganalisis data yang dikumpulkan atau diukur secara berurutan selama periode waktu tertentu. Data time series mencakup observasi atau pengukuran yang dilakukan dalam interval waktu yang teratur. Contoh umum dari time series data termasuk data keuangan harian, data penjualan bulanan, atau data suhu harian.
Peran time series analysis dalam analisis big data sangat penting, terutama dalam konteks bisnis. Beberapa perannya melibatkan:
Prediksi dan Peramalan: Time series analysis memungkinkan perusahaan untuk membuat prediksi dan peramalan berdasarkan data historis. Misalnya, perusahaan dapat menggunakan analisis time series untuk memprediksi penjualan di masa depan, permintaan pelanggan, atau tren pasar.
Optimasi Keputusan: Dengan memahami pola dan tren dalam data time series, perusahaan dapat mengoptimalkan keputusan operasional. Ini mencakup penjadwalan produksi yang lebih baik, manajemen rantai pasokan yang efisien, atau penyesuaian harga yang tepat waktu, dan menetapkan strategi atau desain baru dari produk/service, atau rekomendasi produk baru, dll.
Deteksi Anomali: Time series analysis membantu dalam mendeteksi anomali atau perubahan yang tidak biasa dalam data. Ini dapat membantu perusahaan mengidentifikasi masalah operasional atau potensi risiko lebih awal, seperti gangguan produksi atau perubahan perilaku pelanggan yang tidak biasa.
Pengelolaan Inventori: Dengan memahami pola dalam data time series, perusahaan dapat mengelola inventori dengan lebih efisien, menghindari kekurangan atau kelebihan persediaan yang tidak perlu.
Optimasi Proses Bisnis: Analisis time series dapat digunakan untuk mengoptimalkan proses bisnis, seperti waktu produksi atau waktu pelayanan pelanggan, dengan memahami pola waktu tertentu yang mungkin mempengaruhi efisiensi.
Dengan memanfaatkan time series analysis dalam analisis big data, perusahaan dapat membuat keputusan yang lebih informasional, merencanakan strategi yang lebih baik, dan meningkatkan respons terhadap perubahan pasar atau keadaan bisnis.
Untuk melakukan analisis time series tersebut ada banyak teknik/metode/algoritma/model yang dapat digunakan, berikut beberapa diantaranya:
ARIMA, digunakan untuk tipe data stationary / random
ETS (error, trend, seasonal), sangat mirip pendekatannya dengan prophet facebook, yaitu dengan komponen trend dan seasonality
Bayesian Structural Time Series (BSTS), baik digunakan ketika ada eksternal regressor (atau pengaruh eksternal dari series lain selain komponen time series itu sendiri)
TBATS, model yang bisa digunakan ketika memodelkan “multiple seasonality” yaitu penggunaan 2 macam efek seasonality (misal weekly dan monthly), karena secara umum time series dianggap hanya memiliki 1 tipe seasonality
Prophet adalah model yang dikembangkan oleh Facebook dan fokus pada komponen: trend, seasonality (bisa multiple), dan holiday effect. dll.
Secara umum ada 3 komponen time series yaitu:
Seasonal : data musiman, data dengan pola yang berulang dengan periode yang tetap (tahun, bulan, minggu, hari, jam, detik)
Trend : ada 2 jenis trend yaitu cendrung naik atau cendrung turun
Error : data yang ditangkap oleh Seosonal atau trend yang tidak bisa dijelaskan.
# Library untuk manipulasi data
library (dplyr)
## Warning: package 'dplyr' was built under R version 4.3.3
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
# Library untuk visualisasi data
library (ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.3
library (plotly)
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
# Library model time series forecasting
library (prophet)
## Loading required package: Rcpp
## Loading required package: rlang
# Library untuk split data
library (caTools)
## Warning: package 'caTools' was built under R version 4.3.2
# Library manipulasi tanggal
library (lubridate)
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
sales <- read.csv("data/train.csv")
head(sales)
## date store item sales
## 1 2013-01-01 1 1 13
## 2 2013-01-02 1 1 11
## 3 2013-01-03 1 1 14
## 4 2013-01-04 1 1 13
## 5 2013-01-05 1 1 10
## 6 2013-01-06 1 1 12
# melihat struktur dataset
glimpse (sales)
## Rows: 730,500
## Columns: 4
## $ date <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "2013-01…
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ item <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ sales <int> 13, 11, 14, 13, 10, 12, 10, 9, 12, 9, 9, 7, 10, 12, 5, 7, 16, 7,…
group_sales <- group_by(sales, store)
count(group_sales)
## # A tibble: 10 × 2
## # Groups: store [10]
## store n
## <int> <int>
## 1 1 73050
## 2 2 73050
## 3 3 73050
## 4 4 73050
## 5 5 73050
## 6 6 73050
## 7 7 73050
## 8 8 73050
## 9 9 73050
## 10 10 73050
Bisa dilihat bahwa setiap store memiliki 73050 transaksi.
Sekarang kita akan melihat jumlah transaksi berdasarkan tanggal
transaksi dan kita simpan dalam objek daily_demand
daily_demand <- sales %>%
group_by(date) %>%
summarise(
demand=sum(sales)
)
daily_demand
## # A tibble: 1,461 × 2
## date demand
## <chr> <int>
## 1 2013-01-01 13696
## 2 2013-01-02 13678
## 3 2013-01-03 14488
## 4 2013-01-04 15677
## 5 2013-01-05 16237
## 6 2013-01-06 17291
## 7 2013-01-07 11769
## 8 2013-01-08 13560
## 9 2013-01-09 13878
## 10 2013-01-10 14642
## # ℹ 1,451 more rows
Kita akan mengambil transaksi pada salah satu store saja, misalnya
pada store 3. dan kita simpan dalam objek
daily_demandstore03 dan rubah data dateke type
tanggal (date)
daily_demandstore03 <- sales %>%
filter (store == "3") %>%
mutate (date = as.Date(date)) %>% #merubah type data date
group_by(date) %>%
summarise(
demand=sum(sales)
)
daily_demandstore03
## # A tibble: 1,461 × 2
## date demand
## <date> <int>
## 1 2013-01-01 1588
## 2 2013-01-02 1538
## 3 2013-01-03 1635
## 4 2013-01-04 1741
## 5 2013-01-05 1887
## 6 2013-01-06 1956
## 7 2013-01-07 1313
## 8 2013-01-08 1538
## 9 2013-01-09 1633
## 10 2013-01-10 1677
## # ℹ 1,451 more rows
Bisa dilihat bahwa data date sudah dalam type
tanggal
kita akan memvisualisasi trankasi pada store 03 dari tahun 2013 sampai 2016
plotstore03 <- daily_demandstore03 %>%
ggplot(aes(x = date, y = demand)) +
geom_point(color = "tomato3", group=1) +
labs(
title = "Daily Sales",
subtitle = "Store 03",
caption = "1C Company",
x = "Date",
y = "Total Sales"
) +
theme_minimal()
ggplotly(plotstore03)
Data yang digunakan yaitu data permintaan harian di Store 3 yang
sudah disimpan pada objek daily_demandstore03
daily_demandstore03
## # A tibble: 1,461 × 2
## date demand
## <date> <int>
## 1 2013-01-01 1588
## 2 2013-01-02 1538
## 3 2013-01-03 1635
## 4 2013-01-04 1741
## 5 2013-01-05 1887
## 6 2013-01-06 1956
## 7 2013-01-07 1313
## 8 2013-01-08 1538
## 9 2013-01-09 1633
## 10 2013-01-10 1677
## # ℹ 1,451 more rows
Untuk menggunakan algoritma/model Prophet pertama-tama yang harus dilakukan adalah menyiapkan data frame dengan format: ds untuk menyimpan tanggal, dan y untuk menyimpan dari nilai yang akan prediksi.
# Menyiapkan data
train_daily_3 <- daily_demandstore03 %>%
rename(
ds = "date",
y = "demand"
)
glimpse(train_daily_3)
## Rows: 1,461
## Columns: 2
## $ ds <date> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0…
## $ y <int> 1588, 1538, 1635, 1741, 1887, 1956, 1313, 1538, 1633, 1677, 1831, 1…
Melakukan pemodelan data training dengan menggunakan fungsi
fit.prophet() dimana sebelumnya kita harus menentukan
seasonality nya. dalam kasus ini kita mengggunakan
daily.seasonality
# fitting model data training
model_ts <- prophet(daily.seasonality = TRUE, seasonality_prior_scale=0.1) %>%
fit.prophet(train_daily_3)
model_ts
## $growth
## [1] "linear"
##
## $changepoints
## [1] "2013-02-17 GMT" "2013-04-04 GMT" "2013-05-21 GMT" "2013-07-07 GMT"
## [5] "2013-08-22 GMT" "2013-10-08 GMT" "2013-11-24 GMT" "2014-01-09 GMT"
## [9] "2014-02-25 GMT" "2014-04-13 GMT" "2014-05-29 GMT" "2014-07-15 GMT"
## [13] "2014-08-31 GMT" "2014-10-17 GMT" "2014-12-02 GMT" "2015-01-18 GMT"
## [17] "2015-03-06 GMT" "2015-04-21 GMT" "2015-06-07 GMT" "2015-07-24 GMT"
## [21] "2015-09-08 GMT" "2015-10-25 GMT" "2015-12-11 GMT" "2016-01-26 GMT"
## [25] "2016-03-13 GMT"
##
## $n.changepoints
## [1] 25
##
## $changepoint.range
## [1] 0.8
##
## $yearly.seasonality
## [1] "auto"
##
## $weekly.seasonality
## [1] "auto"
##
## $daily.seasonality
## [1] TRUE
##
## $holidays
## NULL
##
## $seasonality.mode
## [1] "additive"
##
## $seasonality.prior.scale
## [1] 10
##
## $changepoint.prior.scale
## [1] 0.05
##
## $holidays.prior.scale
## [1] 10
##
## $mcmc.samples
## [1] 0
##
## $interval.width
## [1] 0.8
##
## $uncertainty.samples
## [1] 1000
##
## $specified.changepoints
## [1] FALSE
##
## $start
## [1] "2013-01-01 GMT"
##
## $y.scale
## [1] 5004
##
## $logistic.floor
## [1] FALSE
##
## $t.scale
## [1] 126144000
##
## $changepoints.t
## [1] 0.03219178 0.06369863 0.09589041 0.12808219 0.15958904 0.19178082
## [7] 0.22397260 0.25547945 0.28767123 0.31986301 0.35136986 0.38356164
## [13] 0.41575342 0.44794521 0.47945205 0.51164384 0.54383562 0.57534247
## [19] 0.60753425 0.63972603 0.67123288 0.70342466 0.73561644 0.76712329
## [25] 0.79931507
##
## $seasonalities
## $seasonalities$yearly
## $seasonalities$yearly$period
## [1] 365.25
##
## $seasonalities$yearly$fourier.order
## [1] 10
##
## $seasonalities$yearly$prior.scale
## [1] 10
##
## $seasonalities$yearly$mode
## [1] "additive"
##
## $seasonalities$yearly$condition.name
## NULL
##
##
## $seasonalities$weekly
## $seasonalities$weekly$period
## [1] 7
##
## $seasonalities$weekly$fourier.order
## [1] 3
##
## $seasonalities$weekly$prior.scale
## [1] 10
##
## $seasonalities$weekly$mode
## [1] "additive"
##
## $seasonalities$weekly$condition.name
## NULL
##
##
## $seasonalities$daily
## $seasonalities$daily$period
## [1] 1
##
## $seasonalities$daily$fourier.order
## [1] 4
##
## $seasonalities$daily$prior.scale
## [1] 10
##
## $seasonalities$daily$mode
## [1] "additive"
##
## $seasonalities$daily$condition.name
## NULL
##
##
##
## $extra_regressors
## list()
##
## $country_holidays
## NULL
##
## $stan.fit
## $stan.fit$par
## $stan.fit$par$k
## [1] -0.3399185
##
## $stan.fit$par$m
## [1] 0.3551693
##
## $stan.fit$par$delta
## [1] 7.557253e-08 3.483415e-08 2.688660e-01 4.799589e-01 2.004927e-01
## [6] 6.476051e-08 5.903609e-08 -2.108516e-01 -2.755958e-01 -1.215397e-07
## [11] 4.155000e-08 2.488461e-07 -1.266203e-08 -3.357057e-03 -3.749413e-02
## [16] -1.522682e-08 -6.884554e-08 7.239539e-03 2.767627e-02 3.916694e-02
## [21] 7.126680e-02 1.687457e-02 3.888608e-03 1.302859e-07 -6.894206e-02
##
## $stan.fit$par$sigma_obs
## [1] 0.02704036
##
## $stan.fit$par$beta
## [1] -1.503878e-02 -1.395354e-01 -2.416547e-02 -7.901517e-03 -1.777479e-02
## [6] -2.432104e-02 7.693029e-03 -8.147217e-03 6.676297e-03 -1.188980e-02
## [11] 1.535229e-02 3.032079e-03 3.252465e-03 9.647003e-03 4.167203e-03
## [16] 5.074982e-03 -7.422047e-03 5.948540e-03 -4.875237e-03 -4.564492e-04
## [21] 7.696883e-02 -2.570810e-03 -4.462161e-02 -9.995736e-03 4.729456e-02
## [26] 6.687925e-03 -5.405959e-11 3.823590e-02 -1.081192e-10 3.823590e-02
## [31] -2.690668e-11 3.823590e-02 -2.162384e-10 3.823590e-02
##
## $stan.fit$par$trend
## [1] 0.3551693 0.3549365 0.3547037 0.3544709 0.3542380 0.3540052 0.3537724
## [8] 0.3535396 0.3533068 0.3530739 0.3528411 0.3526083 0.3523755 0.3521427
## [15] 0.3519098 0.3516770 0.3514442 0.3512114 0.3509785 0.3507457 0.3505129
## [22] 0.3502801 0.3500473 0.3498144 0.3495816 0.3493488 0.3491160 0.3488832
## [29] 0.3486503 0.3484175 0.3481847 0.3479519 0.3477191 0.3474862 0.3472534
## [36] 0.3470206 0.3467878 0.3465550 0.3463221 0.3460893 0.3458565 0.3456237
## [43] 0.3453908 0.3451580 0.3449252 0.3446924 0.3444596 0.3442267 0.3439939
## [50] 0.3437611 0.3435283 0.3432955 0.3430626 0.3428298 0.3425970 0.3423642
## [57] 0.3421314 0.3418985 0.3416657 0.3414329 0.3412001 0.3409673 0.3407344
## [64] 0.3405016 0.3402688 0.3400360 0.3398031 0.3395703 0.3393375 0.3391047
## [71] 0.3388719 0.3386390 0.3384062 0.3381734 0.3379406 0.3377078 0.3374749
## [78] 0.3372421 0.3370093 0.3367765 0.3365437 0.3363108 0.3360780 0.3358452
## [85] 0.3356124 0.3353796 0.3351467 0.3349139 0.3346811 0.3344483 0.3342154
## [92] 0.3339826 0.3337498 0.3335170 0.3332842 0.3330513 0.3328185 0.3325857
## [99] 0.3323529 0.3321201 0.3318872 0.3316544 0.3314216 0.3311888 0.3309560
## [106] 0.3307231 0.3304903 0.3302575 0.3300247 0.3297919 0.3295590 0.3293262
## [113] 0.3290934 0.3288606 0.3286277 0.3283949 0.3281621 0.3279293 0.3276965
## [120] 0.3274636 0.3272308 0.3269980 0.3267652 0.3265324 0.3262995 0.3260667
## [127] 0.3258339 0.3256011 0.3253683 0.3251354 0.3249026 0.3246698 0.3244370
## [134] 0.3242042 0.3239713 0.3237385 0.3235057 0.3232729 0.3230400 0.3228072
## [141] 0.3225744 0.3225257 0.3224771 0.3224284 0.3223797 0.3223311 0.3222824
## [148] 0.3222337 0.3221851 0.3221364 0.3220877 0.3220391 0.3219904 0.3219417
## [155] 0.3218931 0.3218444 0.3217957 0.3217471 0.3216984 0.3216498 0.3216011
## [162] 0.3215524 0.3215038 0.3214551 0.3214064 0.3213578 0.3213091 0.3212604
## [169] 0.3212118 0.3211631 0.3211144 0.3210658 0.3210171 0.3209684 0.3209198
## [176] 0.3208711 0.3208224 0.3207738 0.3207251 0.3206764 0.3206278 0.3205791
## [183] 0.3205304 0.3204818 0.3204331 0.3203844 0.3203358 0.3202871 0.3205672
## [190] 0.3208472 0.3211273 0.3214074 0.3216875 0.3219675 0.3222476 0.3225277
## [197] 0.3228078 0.3230878 0.3233679 0.3236480 0.3239280 0.3242081 0.3244882
## [204] 0.3247683 0.3250483 0.3253284 0.3256085 0.3258886 0.3261686 0.3264487
## [211] 0.3267288 0.3270089 0.3272889 0.3275690 0.3278491 0.3281291 0.3284092
## [218] 0.3286893 0.3289694 0.3292494 0.3295295 0.3298096 0.3300897 0.3303697
## [225] 0.3306498 0.3309299 0.3312099 0.3314900 0.3317701 0.3320502 0.3323302
## [232] 0.3326103 0.3328904 0.3331705 0.3335879 0.3340052 0.3344226 0.3348400
## [239] 0.3352574 0.3356748 0.3360922 0.3365096 0.3369270 0.3373444 0.3377618
## [246] 0.3381792 0.3385966 0.3390140 0.3394314 0.3398488 0.3402662 0.3406836
## [253] 0.3411010 0.3415184 0.3419358 0.3423532 0.3427706 0.3431880 0.3436054
## [260] 0.3440228 0.3444402 0.3448576 0.3452750 0.3456924 0.3461098 0.3465272
## [267] 0.3469445 0.3473619 0.3477793 0.3481967 0.3486141 0.3490315 0.3494489
## [274] 0.3498663 0.3502837 0.3507011 0.3511185 0.3515359 0.3519533 0.3523707
## [281] 0.3527881 0.3532055 0.3536229 0.3540403 0.3544577 0.3548751 0.3552925
## [288] 0.3557099 0.3561273 0.3565447 0.3569621 0.3573795 0.3577969 0.3582143
## [295] 0.3586317 0.3590491 0.3594665 0.3598838 0.3603012 0.3607186 0.3611360
## [302] 0.3615534 0.3619708 0.3623882 0.3628056 0.3632230 0.3636404 0.3640578
## [309] 0.3644752 0.3648926 0.3653100 0.3657274 0.3661448 0.3665622 0.3669796
## [316] 0.3673970 0.3678144 0.3682318 0.3686492 0.3690666 0.3694840 0.3699014
## [323] 0.3703188 0.3707362 0.3711536 0.3715710 0.3719884 0.3724057 0.3728231
## [330] 0.3732405 0.3736579 0.3740753 0.3744927 0.3749101 0.3753275 0.3757449
## [337] 0.3761623 0.3765797 0.3769971 0.3774145 0.3778319 0.3782493 0.3786667
## [344] 0.3790841 0.3795015 0.3799189 0.3803363 0.3807537 0.3811711 0.3815885
## [351] 0.3820059 0.3824233 0.3828407 0.3832581 0.3836755 0.3840929 0.3845103
## [358] 0.3849277 0.3853451 0.3857624 0.3861798 0.3865972 0.3870146 0.3874320
## [365] 0.3878494 0.3882668 0.3886842 0.3891016 0.3895190 0.3899364 0.3903538
## [372] 0.3907712 0.3911886 0.3916060 0.3918790 0.3921520 0.3924249 0.3926979
## [379] 0.3929709 0.3932439 0.3935168 0.3937898 0.3940628 0.3943358 0.3946088
## [386] 0.3948817 0.3951547 0.3954277 0.3957007 0.3959736 0.3962466 0.3965196
## [393] 0.3967926 0.3970656 0.3973385 0.3976115 0.3978845 0.3981575 0.3984305
## [400] 0.3987034 0.3989764 0.3992494 0.3995224 0.3997953 0.4000683 0.4003413
## [407] 0.4006143 0.4008873 0.4011602 0.4014332 0.4017062 0.4019792 0.4022521
## [414] 0.4025251 0.4027981 0.4030711 0.4033441 0.4036170 0.4038900 0.4041630
## [421] 0.4044360 0.4045202 0.4046044 0.4046886 0.4047728 0.4048570 0.4049412
## [428] 0.4050255 0.4051097 0.4051939 0.4052781 0.4053623 0.4054465 0.4055307
## [435] 0.4056150 0.4056992 0.4057834 0.4058676 0.4059518 0.4060360 0.4061202
## [442] 0.4062045 0.4062887 0.4063729 0.4064571 0.4065413 0.4066255 0.4067097
## [449] 0.4067939 0.4068782 0.4069624 0.4070466 0.4071308 0.4072150 0.4072992
## [456] 0.4073834 0.4074677 0.4075519 0.4076361 0.4077203 0.4078045 0.4078887
## [463] 0.4079729 0.4080572 0.4081414 0.4082256 0.4083098 0.4083940 0.4084782
## [470] 0.4085624 0.4086466 0.4087309 0.4088151 0.4088993 0.4089835 0.4090677
## [477] 0.4091519 0.4092361 0.4093204 0.4094046 0.4094888 0.4095730 0.4096572
## [484] 0.4097414 0.4098256 0.4099099 0.4099941 0.4100783 0.4101625 0.4102467
## [491] 0.4103309 0.4104151 0.4104993 0.4105836 0.4106678 0.4107520 0.4108362
## [498] 0.4109204 0.4110046 0.4110888 0.4111731 0.4112573 0.4113415 0.4114257
## [505] 0.4115099 0.4115941 0.4116783 0.4117626 0.4118468 0.4119310 0.4120152
## [512] 0.4120994 0.4121836 0.4122678 0.4123520 0.4124363 0.4125205 0.4126047
## [519] 0.4126889 0.4127731 0.4128573 0.4129415 0.4130258 0.4131100 0.4131942
## [526] 0.4132784 0.4133626 0.4134468 0.4135310 0.4136153 0.4136995 0.4137837
## [533] 0.4138679 0.4139521 0.4140363 0.4141205 0.4142047 0.4142890 0.4143732
## [540] 0.4144574 0.4145416 0.4146258 0.4147100 0.4147942 0.4148785 0.4149627
## [547] 0.4150469 0.4151311 0.4152153 0.4152995 0.4153837 0.4154679 0.4155522
## [554] 0.4156364 0.4157206 0.4158048 0.4158890 0.4159732 0.4160574 0.4161417
## [561] 0.4162259 0.4163101 0.4163943 0.4164785 0.4165627 0.4166469 0.4167312
## [568] 0.4168154 0.4168996 0.4169838 0.4170680 0.4171522 0.4172364 0.4173207
## [575] 0.4174049 0.4174891 0.4175733 0.4176575 0.4177417 0.4178259 0.4179101
## [582] 0.4179944 0.4180786 0.4181628 0.4182470 0.4183312 0.4184154 0.4184996
## [589] 0.4185839 0.4186681 0.4187523 0.4188365 0.4189207 0.4190049 0.4190891
## [596] 0.4191734 0.4192576 0.4193418 0.4194260 0.4195102 0.4195944 0.4196786
## [603] 0.4197629 0.4198471 0.4199313 0.4200155 0.4200997 0.4201839 0.4202681
## [610] 0.4203523 0.4204366 0.4205208 0.4206050 0.4206892 0.4207734 0.4208576
## [617] 0.4209418 0.4210261 0.4211103 0.4211945 0.4212787 0.4213629 0.4214471
## [624] 0.4215313 0.4216156 0.4216998 0.4217840 0.4218682 0.4219524 0.4220366
## [631] 0.4221208 0.4222051 0.4222893 0.4223735 0.4224577 0.4225419 0.4226261
## [638] 0.4227103 0.4227945 0.4228788 0.4229630 0.4230472 0.4231314 0.4232156
## [645] 0.4232998 0.4233840 0.4234683 0.4235525 0.4236367 0.4237209 0.4238051
## [652] 0.4238893 0.4239735 0.4240578 0.4241420 0.4242239 0.4243058 0.4243877
## [659] 0.4244696 0.4245515 0.4246335 0.4247154 0.4247973 0.4248792 0.4249611
## [666] 0.4250430 0.4251249 0.4252069 0.4252888 0.4253707 0.4254526 0.4255345
## [673] 0.4256164 0.4256983 0.4257803 0.4258622 0.4259441 0.4260260 0.4261079
## [680] 0.4261898 0.4262717 0.4263537 0.4264356 0.4265175 0.4265994 0.4266813
## [687] 0.4267632 0.4268451 0.4269271 0.4270090 0.4270909 0.4271728 0.4272547
## [694] 0.4273366 0.4274185 0.4275005 0.4275824 0.4276643 0.4277462 0.4278281
## [701] 0.4279100 0.4279663 0.4280225 0.4280787 0.4281350 0.4281912 0.4282474
## [708] 0.4283037 0.4283599 0.4284161 0.4284724 0.4285286 0.4285848 0.4286411
## [715] 0.4286973 0.4287535 0.4288098 0.4288660 0.4289222 0.4289785 0.4290347
## [722] 0.4290909 0.4291472 0.4292034 0.4292596 0.4293159 0.4293721 0.4294283
## [729] 0.4294846 0.4295408 0.4295970 0.4296533 0.4297095 0.4297657 0.4298220
## [736] 0.4298782 0.4299344 0.4299907 0.4300469 0.4301031 0.4301594 0.4302156
## [743] 0.4302718 0.4303281 0.4303843 0.4304405 0.4304968 0.4305530 0.4306092
## [750] 0.4306655 0.4307217 0.4307779 0.4308342 0.4308904 0.4309466 0.4310029
## [757] 0.4310591 0.4311153 0.4311716 0.4312278 0.4312840 0.4313403 0.4313965
## [764] 0.4314527 0.4315090 0.4315652 0.4316214 0.4316777 0.4317339 0.4317901
## [771] 0.4318464 0.4319026 0.4319588 0.4320151 0.4320713 0.4321275 0.4321838
## [778] 0.4322400 0.4322962 0.4323525 0.4324087 0.4324649 0.4325212 0.4325774
## [785] 0.4326336 0.4326899 0.4327461 0.4328023 0.4328586 0.4329148 0.4329710
## [792] 0.4330273 0.4330835 0.4331397 0.4331960 0.4332522 0.4333084 0.4333647
## [799] 0.4334209 0.4334771 0.4335334 0.4335896 0.4336458 0.4337021 0.4337583
## [806] 0.4338145 0.4338708 0.4339270 0.4339832 0.4340395 0.4340957 0.4341520
## [813] 0.4342082 0.4342644 0.4343207 0.4343769 0.4344331 0.4344894 0.4345456
## [820] 0.4346018 0.4346581 0.4347143 0.4347705 0.4348268 0.4348830 0.4349392
## [827] 0.4349955 0.4350517 0.4351079 0.4351642 0.4352204 0.4352766 0.4353329
## [834] 0.4353891 0.4354453 0.4355016 0.4355578 0.4356140 0.4356703 0.4357265
## [841] 0.4357827 0.4358439 0.4359051 0.4359663 0.4360275 0.4360887 0.4361499
## [848] 0.4362111 0.4362723 0.4363334 0.4363946 0.4364558 0.4365170 0.4365782
## [855] 0.4366394 0.4367006 0.4367618 0.4368230 0.4368842 0.4369454 0.4370066
## [862] 0.4370678 0.4371289 0.4371901 0.4372513 0.4373125 0.4373737 0.4374349
## [869] 0.4374961 0.4375573 0.4376185 0.4376797 0.4377409 0.4378021 0.4378632
## [876] 0.4379244 0.4379856 0.4380468 0.4381080 0.4381692 0.4382304 0.4382916
## [883] 0.4383528 0.4384140 0.4384752 0.4385364 0.4385976 0.4386587 0.4387389
## [890] 0.4388190 0.4388992 0.4389793 0.4390595 0.4391396 0.4392198 0.4392999
## [897] 0.4393801 0.4394602 0.4395404 0.4396205 0.4397007 0.4397808 0.4398610
## [904] 0.4399411 0.4400213 0.4401014 0.4401816 0.4402617 0.4403419 0.4404220
## [911] 0.4405022 0.4405823 0.4406625 0.4407426 0.4408228 0.4409029 0.4409830
## [918] 0.4410632 0.4411433 0.4412235 0.4413036 0.4413838 0.4414639 0.4415441
## [925] 0.4416242 0.4417044 0.4417845 0.4418647 0.4419448 0.4420250 0.4421051
## [932] 0.4421853 0.4422654 0.4423456 0.4424257 0.4425327 0.4426397 0.4427466
## [939] 0.4428536 0.4429606 0.4430676 0.4431745 0.4432815 0.4433885 0.4434955
## [946] 0.4436024 0.4437094 0.4438164 0.4439234 0.4440303 0.4441373 0.4442443
## [953] 0.4443513 0.4444582 0.4445652 0.4446722 0.4447792 0.4448861 0.4449931
## [960] 0.4451001 0.4452071 0.4453140 0.4454210 0.4455280 0.4456350 0.4457419
## [967] 0.4458489 0.4459559 0.4460629 0.4461698 0.4462768 0.4463838 0.4464908
## [974] 0.4465977 0.4467047 0.4468117 0.4469187 0.4470256 0.4471326 0.4472396
## [981] 0.4473466 0.4475024 0.4476581 0.4478139 0.4479697 0.4481255 0.4482813
## [988] 0.4484371 0.4485929 0.4487487 0.4489045 0.4490602 0.4492160 0.4493718
## [995] 0.4495276 0.4496834 0.4498392 0.4499950 0.4501508 0.4503065 0.4504623
## [1002] 0.4506181 0.4507739 0.4509297 0.4510855 0.4512413 0.4513971 0.4515528
## [1009] 0.4517086 0.4518644 0.4520202 0.4521760 0.4523318 0.4524876 0.4526434
## [1016] 0.4527992 0.4529549 0.4531107 0.4532665 0.4534223 0.4535781 0.4537339
## [1023] 0.4538897 0.4540455 0.4542012 0.4543570 0.4545128 0.4546686 0.4548360
## [1030] 0.4550033 0.4551706 0.4553380 0.4555053 0.4556727 0.4558400 0.4560074
## [1037] 0.4561747 0.4563421 0.4565094 0.4566768 0.4568441 0.4570114 0.4571788
## [1044] 0.4573461 0.4575135 0.4576808 0.4578482 0.4580155 0.4581829 0.4583502
## [1051] 0.4585176 0.4586849 0.4588523 0.4590196 0.4591869 0.4593543 0.4595216
## [1058] 0.4596890 0.4598563 0.4600237 0.4601910 0.4603584 0.4605257 0.4606931
## [1065] 0.4608604 0.4610277 0.4611951 0.4613624 0.4615298 0.4616971 0.4618645
## [1072] 0.4620318 0.4621992 0.4623665 0.4625339 0.4627039 0.4628739 0.4630439
## [1079] 0.4632139 0.4633839 0.4635539 0.4637239 0.4638939 0.4640639 0.4642340
## [1086] 0.4644040 0.4645740 0.4647440 0.4649140 0.4650840 0.4652540 0.4654240
## [1093] 0.4655940 0.4657640 0.4659340 0.4661041 0.4662741 0.4664441 0.4666141
## [1100] 0.4667841 0.4669541 0.4671241 0.4672941 0.4674641 0.4676341 0.4678042
## [1107] 0.4679742 0.4681442 0.4683142 0.4684842 0.4686542 0.4688242 0.4689942
## [1114] 0.4691642 0.4693342 0.4695042 0.4696743 0.4698443 0.4700143 0.4701843
## [1121] 0.4703543 0.4705243 0.4706943 0.4708643 0.4710343 0.4712043 0.4713743
## [1128] 0.4715444 0.4717144 0.4718844 0.4720544 0.4722244 0.4723944 0.4725644
## [1135] 0.4727344 0.4729044 0.4730744 0.4732444 0.4734145 0.4735845 0.4737545
## [1142] 0.4739245 0.4740945 0.4742645 0.4744345 0.4746045 0.4747745 0.4749445
## [1149] 0.4751146 0.4752846 0.4754546 0.4756246 0.4757946 0.4759646 0.4761346
## [1156] 0.4763046 0.4764746 0.4766446 0.4768146 0.4769847 0.4771547 0.4773247
## [1163] 0.4774947 0.4776647 0.4778347 0.4780047 0.4781747 0.4783447 0.4784675
## [1170] 0.4785903 0.4787131 0.4788359 0.4789587 0.4790815 0.4792043 0.4793270
## [1177] 0.4794498 0.4795726 0.4796954 0.4798182 0.4799410 0.4800638 0.4801866
## [1184] 0.4803094 0.4804321 0.4805549 0.4806777 0.4808005 0.4809233 0.4810461
## [1191] 0.4811689 0.4812917 0.4814145 0.4815372 0.4816600 0.4817828 0.4819056
## [1198] 0.4820284 0.4821512 0.4822740 0.4823968 0.4825195 0.4826423 0.4827651
## [1205] 0.4828879 0.4830107 0.4831335 0.4832563 0.4833791 0.4835019 0.4836246
## [1212] 0.4837474 0.4838702 0.4839930 0.4841158 0.4842386 0.4843614 0.4844842
## [1219] 0.4846070 0.4847297 0.4848525 0.4849753 0.4850981 0.4852209 0.4853437
## [1226] 0.4854665 0.4855893 0.4857121 0.4858348 0.4859576 0.4860804 0.4862032
## [1233] 0.4863260 0.4864488 0.4865716 0.4866944 0.4868172 0.4869399 0.4870627
## [1240] 0.4871855 0.4873083 0.4874311 0.4875539 0.4876767 0.4877995 0.4879223
## [1247] 0.4880450 0.4881678 0.4882906 0.4884134 0.4885362 0.4886590 0.4887818
## [1254] 0.4889046 0.4890274 0.4891501 0.4892729 0.4893957 0.4895185 0.4896413
## [1261] 0.4897641 0.4898869 0.4900097 0.4901325 0.4902552 0.4903780 0.4905008
## [1268] 0.4906236 0.4907464 0.4908692 0.4909920 0.4911148 0.4912376 0.4913603
## [1275] 0.4914831 0.4916059 0.4917287 0.4918515 0.4919743 0.4920971 0.4922199
## [1282] 0.4923427 0.4924654 0.4925882 0.4927110 0.4928338 0.4929566 0.4930794
## [1289] 0.4932022 0.4933250 0.4934478 0.4935705 0.4936933 0.4938161 0.4939389
## [1296] 0.4940617 0.4941845 0.4943073 0.4944301 0.4945529 0.4946756 0.4947984
## [1303] 0.4949212 0.4950440 0.4951668 0.4952896 0.4954124 0.4955352 0.4956580
## [1310] 0.4957807 0.4959035 0.4960263 0.4961491 0.4962719 0.4963947 0.4965175
## [1317] 0.4966403 0.4967630 0.4968858 0.4970086 0.4971314 0.4972542 0.4973770
## [1324] 0.4974998 0.4976226 0.4977454 0.4978681 0.4979909 0.4981137 0.4982365
## [1331] 0.4983593 0.4984821 0.4986049 0.4987277 0.4988505 0.4989732 0.4990960
## [1338] 0.4992188 0.4993416 0.4994644 0.4995872 0.4997100 0.4998328 0.4999556
## [1345] 0.5000783 0.5002011 0.5003239 0.5004467 0.5005695 0.5006923 0.5008151
## [1352] 0.5009379 0.5010607 0.5011834 0.5013062 0.5014290 0.5015518 0.5016746
## [1359] 0.5017974 0.5019202 0.5020430 0.5021658 0.5022885 0.5024113 0.5025341
## [1366] 0.5026569 0.5027797 0.5029025 0.5030253 0.5031481 0.5032709 0.5033936
## [1373] 0.5035164 0.5036392 0.5037620 0.5038848 0.5040076 0.5041304 0.5042532
## [1380] 0.5043760 0.5044987 0.5046215 0.5047443 0.5048671 0.5049899 0.5051127
## [1387] 0.5052355 0.5053583 0.5054811 0.5056038 0.5057266 0.5058494 0.5059722
## [1394] 0.5060950 0.5062178 0.5063406 0.5064634 0.5065862 0.5067089 0.5068317
## [1401] 0.5069545 0.5070773 0.5072001 0.5073229 0.5074457 0.5075685 0.5076913
## [1408] 0.5078140 0.5079368 0.5080596 0.5081824 0.5083052 0.5084280 0.5085508
## [1415] 0.5086736 0.5087964 0.5089191 0.5090419 0.5091647 0.5092875 0.5094103
## [1422] 0.5095331 0.5096559 0.5097787 0.5099015 0.5100242 0.5101470 0.5102698
## [1429] 0.5103926 0.5105154 0.5106382 0.5107610 0.5108838 0.5110065 0.5111293
## [1436] 0.5112521 0.5113749 0.5114977 0.5116205 0.5117433 0.5118661 0.5119889
## [1443] 0.5121116 0.5122344 0.5123572 0.5124800 0.5126028 0.5127256 0.5128484
## [1450] 0.5129712 0.5130940 0.5132167 0.5133395 0.5134623 0.5135851 0.5137079
## [1457] 0.5138307 0.5139535 0.5140763 0.5141991 0.5143218
##
##
## $stan.fit$value
## [1] 4510.037
##
## $stan.fit$return_code
## [1] 0
##
## $stan.fit$theta_tilde
## k m delta[1] delta[2] delta[3] delta[4]
## [1,] -0.3399185 0.3551693 7.557253e-08 3.483415e-08 0.268866 0.4799589
## delta[5] delta[6] delta[7] delta[8] delta[9] delta[10]
## [1,] 0.2004927 6.476051e-08 5.903609e-08 -0.2108516 -0.2755958 -1.215397e-07
## delta[11] delta[12] delta[13] delta[14] delta[15]
## [1,] 4.155e-08 2.488461e-07 -1.266203e-08 -0.003357057 -0.03749413
## delta[16] delta[17] delta[18] delta[19] delta[20] delta[21]
## [1,] -1.522682e-08 -6.884554e-08 0.007239539 0.02767627 0.03916694 0.0712668
## delta[22] delta[23] delta[24] delta[25] sigma_obs beta[1]
## [1,] 0.01687457 0.003888608 1.302859e-07 -0.06894206 0.02704036 -0.01503878
## beta[2] beta[3] beta[4] beta[5] beta[6] beta[7]
## [1,] -0.1395354 -0.02416547 -0.007901517 -0.01777479 -0.02432104 0.007693029
## beta[8] beta[9] beta[10] beta[11] beta[12] beta[13]
## [1,] -0.008147217 0.006676297 -0.0118898 0.01535229 0.003032079 0.003252465
## beta[14] beta[15] beta[16] beta[17] beta[18] beta[19]
## [1,] 0.009647003 0.004167203 0.005074982 -0.007422047 0.00594854 -0.004875237
## beta[20] beta[21] beta[22] beta[23] beta[24] beta[25]
## [1,] -0.0004564492 0.07696883 -0.00257081 -0.04462161 -0.009995736 0.04729456
## beta[26] beta[27] beta[28] beta[29] beta[30] beta[31]
## [1,] 0.006687925 -5.405959e-11 0.0382359 -1.081192e-10 0.0382359 -2.690668e-11
## beta[32] beta[33] beta[34] trend[1] trend[2] trend[3] trend[4]
## [1,] 0.0382359 -2.162384e-10 0.0382359 0.3551693 0.3549365 0.3547037 0.3544709
## trend[5] trend[6] trend[7] trend[8] trend[9] trend[10] trend[11]
## [1,] 0.354238 0.3540052 0.3537724 0.3535396 0.3533068 0.3530739 0.3528411
## trend[12] trend[13] trend[14] trend[15] trend[16] trend[17] trend[18]
## [1,] 0.3526083 0.3523755 0.3521427 0.3519098 0.351677 0.3514442 0.3512114
## trend[19] trend[20] trend[21] trend[22] trend[23] trend[24] trend[25]
## [1,] 0.3509785 0.3507457 0.3505129 0.3502801 0.3500473 0.3498144 0.3495816
## trend[26] trend[27] trend[28] trend[29] trend[30] trend[31] trend[32]
## [1,] 0.3493488 0.349116 0.3488832 0.3486503 0.3484175 0.3481847 0.3479519
## trend[33] trend[34] trend[35] trend[36] trend[37] trend[38] trend[39]
## [1,] 0.3477191 0.3474862 0.3472534 0.3470206 0.3467878 0.346555 0.3463221
## trend[40] trend[41] trend[42] trend[43] trend[44] trend[45] trend[46]
## [1,] 0.3460893 0.3458565 0.3456237 0.3453908 0.345158 0.3449252 0.3446924
## trend[47] trend[48] trend[49] trend[50] trend[51] trend[52] trend[53]
## [1,] 0.3444596 0.3442267 0.3439939 0.3437611 0.3435283 0.3432955 0.3430626
## trend[54] trend[55] trend[56] trend[57] trend[58] trend[59] trend[60]
## [1,] 0.3428298 0.342597 0.3423642 0.3421314 0.3418985 0.3416657 0.3414329
## trend[61] trend[62] trend[63] trend[64] trend[65] trend[66] trend[67]
## [1,] 0.3412001 0.3409673 0.3407344 0.3405016 0.3402688 0.340036 0.3398031
## trend[68] trend[69] trend[70] trend[71] trend[72] trend[73] trend[74]
## [1,] 0.3395703 0.3393375 0.3391047 0.3388719 0.338639 0.3384062 0.3381734
## trend[75] trend[76] trend[77] trend[78] trend[79] trend[80] trend[81]
## [1,] 0.3379406 0.3377078 0.3374749 0.3372421 0.3370093 0.3367765 0.3365437
## trend[82] trend[83] trend[84] trend[85] trend[86] trend[87] trend[88]
## [1,] 0.3363108 0.336078 0.3358452 0.3356124 0.3353796 0.3351467 0.3349139
## trend[89] trend[90] trend[91] trend[92] trend[93] trend[94] trend[95]
## [1,] 0.3346811 0.3344483 0.3342154 0.3339826 0.3337498 0.333517 0.3332842
## trend[96] trend[97] trend[98] trend[99] trend[100] trend[101] trend[102]
## [1,] 0.3330513 0.3328185 0.3325857 0.3323529 0.3321201 0.3318872 0.3316544
## trend[103] trend[104] trend[105] trend[106] trend[107] trend[108]
## [1,] 0.3314216 0.3311888 0.330956 0.3307231 0.3304903 0.3302575
## trend[109] trend[110] trend[111] trend[112] trend[113] trend[114]
## [1,] 0.3300247 0.3297919 0.329559 0.3293262 0.3290934 0.3288606
## trend[115] trend[116] trend[117] trend[118] trend[119] trend[120]
## [1,] 0.3286277 0.3283949 0.3281621 0.3279293 0.3276965 0.3274636
## trend[121] trend[122] trend[123] trend[124] trend[125] trend[126]
## [1,] 0.3272308 0.326998 0.3267652 0.3265324 0.3262995 0.3260667
## trend[127] trend[128] trend[129] trend[130] trend[131] trend[132]
## [1,] 0.3258339 0.3256011 0.3253683 0.3251354 0.3249026 0.3246698
## trend[133] trend[134] trend[135] trend[136] trend[137] trend[138]
## [1,] 0.324437 0.3242042 0.3239713 0.3237385 0.3235057 0.3232729
## trend[139] trend[140] trend[141] trend[142] trend[143] trend[144]
## [1,] 0.32304 0.3228072 0.3225744 0.3225257 0.3224771 0.3224284
## trend[145] trend[146] trend[147] trend[148] trend[149] trend[150]
## [1,] 0.3223797 0.3223311 0.3222824 0.3222337 0.3221851 0.3221364
## trend[151] trend[152] trend[153] trend[154] trend[155] trend[156]
## [1,] 0.3220877 0.3220391 0.3219904 0.3219417 0.3218931 0.3218444
## trend[157] trend[158] trend[159] trend[160] trend[161] trend[162]
## [1,] 0.3217957 0.3217471 0.3216984 0.3216498 0.3216011 0.3215524
## trend[163] trend[164] trend[165] trend[166] trend[167] trend[168]
## [1,] 0.3215038 0.3214551 0.3214064 0.3213578 0.3213091 0.3212604
## trend[169] trend[170] trend[171] trend[172] trend[173] trend[174]
## [1,] 0.3212118 0.3211631 0.3211144 0.3210658 0.3210171 0.3209684
## trend[175] trend[176] trend[177] trend[178] trend[179] trend[180]
## [1,] 0.3209198 0.3208711 0.3208224 0.3207738 0.3207251 0.3206764
## trend[181] trend[182] trend[183] trend[184] trend[185] trend[186]
## [1,] 0.3206278 0.3205791 0.3205304 0.3204818 0.3204331 0.3203844
## trend[187] trend[188] trend[189] trend[190] trend[191] trend[192]
## [1,] 0.3203358 0.3202871 0.3205672 0.3208472 0.3211273 0.3214074
## trend[193] trend[194] trend[195] trend[196] trend[197] trend[198]
## [1,] 0.3216875 0.3219675 0.3222476 0.3225277 0.3228078 0.3230878
## trend[199] trend[200] trend[201] trend[202] trend[203] trend[204]
## [1,] 0.3233679 0.323648 0.323928 0.3242081 0.3244882 0.3247683
## trend[205] trend[206] trend[207] trend[208] trend[209] trend[210]
## [1,] 0.3250483 0.3253284 0.3256085 0.3258886 0.3261686 0.3264487
## trend[211] trend[212] trend[213] trend[214] trend[215] trend[216]
## [1,] 0.3267288 0.3270089 0.3272889 0.327569 0.3278491 0.3281291
## trend[217] trend[218] trend[219] trend[220] trend[221] trend[222]
## [1,] 0.3284092 0.3286893 0.3289694 0.3292494 0.3295295 0.3298096
## trend[223] trend[224] trend[225] trend[226] trend[227] trend[228]
## [1,] 0.3300897 0.3303697 0.3306498 0.3309299 0.3312099 0.33149
## trend[229] trend[230] trend[231] trend[232] trend[233] trend[234]
## [1,] 0.3317701 0.3320502 0.3323302 0.3326103 0.3328904 0.3331705
## trend[235] trend[236] trend[237] trend[238] trend[239] trend[240]
## [1,] 0.3335879 0.3340052 0.3344226 0.33484 0.3352574 0.3356748
## trend[241] trend[242] trend[243] trend[244] trend[245] trend[246]
## [1,] 0.3360922 0.3365096 0.336927 0.3373444 0.3377618 0.3381792
## trend[247] trend[248] trend[249] trend[250] trend[251] trend[252]
## [1,] 0.3385966 0.339014 0.3394314 0.3398488 0.3402662 0.3406836
## trend[253] trend[254] trend[255] trend[256] trend[257] trend[258]
## [1,] 0.341101 0.3415184 0.3419358 0.3423532 0.3427706 0.343188
## trend[259] trend[260] trend[261] trend[262] trend[263] trend[264]
## [1,] 0.3436054 0.3440228 0.3444402 0.3448576 0.345275 0.3456924
## trend[265] trend[266] trend[267] trend[268] trend[269] trend[270]
## [1,] 0.3461098 0.3465272 0.3469445 0.3473619 0.3477793 0.3481967
## trend[271] trend[272] trend[273] trend[274] trend[275] trend[276]
## [1,] 0.3486141 0.3490315 0.3494489 0.3498663 0.3502837 0.3507011
## trend[277] trend[278] trend[279] trend[280] trend[281] trend[282]
## [1,] 0.3511185 0.3515359 0.3519533 0.3523707 0.3527881 0.3532055
## trend[283] trend[284] trend[285] trend[286] trend[287] trend[288]
## [1,] 0.3536229 0.3540403 0.3544577 0.3548751 0.3552925 0.3557099
## trend[289] trend[290] trend[291] trend[292] trend[293] trend[294]
## [1,] 0.3561273 0.3565447 0.3569621 0.3573795 0.3577969 0.3582143
## trend[295] trend[296] trend[297] trend[298] trend[299] trend[300]
## [1,] 0.3586317 0.3590491 0.3594665 0.3598838 0.3603012 0.3607186
## trend[301] trend[302] trend[303] trend[304] trend[305] trend[306]
## [1,] 0.361136 0.3615534 0.3619708 0.3623882 0.3628056 0.363223
## trend[307] trend[308] trend[309] trend[310] trend[311] trend[312]
## [1,] 0.3636404 0.3640578 0.3644752 0.3648926 0.36531 0.3657274
## trend[313] trend[314] trend[315] trend[316] trend[317] trend[318]
## [1,] 0.3661448 0.3665622 0.3669796 0.367397 0.3678144 0.3682318
## trend[319] trend[320] trend[321] trend[322] trend[323] trend[324]
## [1,] 0.3686492 0.3690666 0.369484 0.3699014 0.3703188 0.3707362
## trend[325] trend[326] trend[327] trend[328] trend[329] trend[330]
## [1,] 0.3711536 0.371571 0.3719884 0.3724057 0.3728231 0.3732405
## trend[331] trend[332] trend[333] trend[334] trend[335] trend[336]
## [1,] 0.3736579 0.3740753 0.3744927 0.3749101 0.3753275 0.3757449
## trend[337] trend[338] trend[339] trend[340] trend[341] trend[342]
## [1,] 0.3761623 0.3765797 0.3769971 0.3774145 0.3778319 0.3782493
## trend[343] trend[344] trend[345] trend[346] trend[347] trend[348]
## [1,] 0.3786667 0.3790841 0.3795015 0.3799189 0.3803363 0.3807537
## trend[349] trend[350] trend[351] trend[352] trend[353] trend[354]
## [1,] 0.3811711 0.3815885 0.3820059 0.3824233 0.3828407 0.3832581
## trend[355] trend[356] trend[357] trend[358] trend[359] trend[360]
## [1,] 0.3836755 0.3840929 0.3845103 0.3849277 0.3853451 0.3857624
## trend[361] trend[362] trend[363] trend[364] trend[365] trend[366]
## [1,] 0.3861798 0.3865972 0.3870146 0.387432 0.3878494 0.3882668
## trend[367] trend[368] trend[369] trend[370] trend[371] trend[372]
## [1,] 0.3886842 0.3891016 0.389519 0.3899364 0.3903538 0.3907712
## trend[373] trend[374] trend[375] trend[376] trend[377] trend[378]
## [1,] 0.3911886 0.391606 0.391879 0.392152 0.3924249 0.3926979
## trend[379] trend[380] trend[381] trend[382] trend[383] trend[384]
## [1,] 0.3929709 0.3932439 0.3935168 0.3937898 0.3940628 0.3943358
## trend[385] trend[386] trend[387] trend[388] trend[389] trend[390]
## [1,] 0.3946088 0.3948817 0.3951547 0.3954277 0.3957007 0.3959736
## trend[391] trend[392] trend[393] trend[394] trend[395] trend[396]
## [1,] 0.3962466 0.3965196 0.3967926 0.3970656 0.3973385 0.3976115
## trend[397] trend[398] trend[399] trend[400] trend[401] trend[402]
## [1,] 0.3978845 0.3981575 0.3984305 0.3987034 0.3989764 0.3992494
## trend[403] trend[404] trend[405] trend[406] trend[407] trend[408]
## [1,] 0.3995224 0.3997953 0.4000683 0.4003413 0.4006143 0.4008873
## trend[409] trend[410] trend[411] trend[412] trend[413] trend[414]
## [1,] 0.4011602 0.4014332 0.4017062 0.4019792 0.4022521 0.4025251
## trend[415] trend[416] trend[417] trend[418] trend[419] trend[420]
## [1,] 0.4027981 0.4030711 0.4033441 0.403617 0.40389 0.404163
## trend[421] trend[422] trend[423] trend[424] trend[425] trend[426]
## [1,] 0.404436 0.4045202 0.4046044 0.4046886 0.4047728 0.404857
## trend[427] trend[428] trend[429] trend[430] trend[431] trend[432]
## [1,] 0.4049412 0.4050255 0.4051097 0.4051939 0.4052781 0.4053623
## trend[433] trend[434] trend[435] trend[436] trend[437] trend[438]
## [1,] 0.4054465 0.4055307 0.405615 0.4056992 0.4057834 0.4058676
## trend[439] trend[440] trend[441] trend[442] trend[443] trend[444]
## [1,] 0.4059518 0.406036 0.4061202 0.4062045 0.4062887 0.4063729
## trend[445] trend[446] trend[447] trend[448] trend[449] trend[450]
## [1,] 0.4064571 0.4065413 0.4066255 0.4067097 0.4067939 0.4068782
## trend[451] trend[452] trend[453] trend[454] trend[455] trend[456]
## [1,] 0.4069624 0.4070466 0.4071308 0.407215 0.4072992 0.4073834
## trend[457] trend[458] trend[459] trend[460] trend[461] trend[462]
## [1,] 0.4074677 0.4075519 0.4076361 0.4077203 0.4078045 0.4078887
## trend[463] trend[464] trend[465] trend[466] trend[467] trend[468]
## [1,] 0.4079729 0.4080572 0.4081414 0.4082256 0.4083098 0.408394
## trend[469] trend[470] trend[471] trend[472] trend[473] trend[474]
## [1,] 0.4084782 0.4085624 0.4086466 0.4087309 0.4088151 0.4088993
## trend[475] trend[476] trend[477] trend[478] trend[479] trend[480]
## [1,] 0.4089835 0.4090677 0.4091519 0.4092361 0.4093204 0.4094046
## trend[481] trend[482] trend[483] trend[484] trend[485] trend[486]
## [1,] 0.4094888 0.409573 0.4096572 0.4097414 0.4098256 0.4099099
## trend[487] trend[488] trend[489] trend[490] trend[491] trend[492]
## [1,] 0.4099941 0.4100783 0.4101625 0.4102467 0.4103309 0.4104151
## trend[493] trend[494] trend[495] trend[496] trend[497] trend[498]
## [1,] 0.4104993 0.4105836 0.4106678 0.410752 0.4108362 0.4109204
## trend[499] trend[500] trend[501] trend[502] trend[503] trend[504]
## [1,] 0.4110046 0.4110888 0.4111731 0.4112573 0.4113415 0.4114257
## trend[505] trend[506] trend[507] trend[508] trend[509] trend[510]
## [1,] 0.4115099 0.4115941 0.4116783 0.4117626 0.4118468 0.411931
## trend[511] trend[512] trend[513] trend[514] trend[515] trend[516]
## [1,] 0.4120152 0.4120994 0.4121836 0.4122678 0.412352 0.4124363
## trend[517] trend[518] trend[519] trend[520] trend[521] trend[522]
## [1,] 0.4125205 0.4126047 0.4126889 0.4127731 0.4128573 0.4129415
## trend[523] trend[524] trend[525] trend[526] trend[527] trend[528]
## [1,] 0.4130258 0.41311 0.4131942 0.4132784 0.4133626 0.4134468
## trend[529] trend[530] trend[531] trend[532] trend[533] trend[534]
## [1,] 0.413531 0.4136153 0.4136995 0.4137837 0.4138679 0.4139521
## trend[535] trend[536] trend[537] trend[538] trend[539] trend[540]
## [1,] 0.4140363 0.4141205 0.4142047 0.414289 0.4143732 0.4144574
## trend[541] trend[542] trend[543] trend[544] trend[545] trend[546]
## [1,] 0.4145416 0.4146258 0.41471 0.4147942 0.4148785 0.4149627
## trend[547] trend[548] trend[549] trend[550] trend[551] trend[552]
## [1,] 0.4150469 0.4151311 0.4152153 0.4152995 0.4153837 0.4154679
## trend[553] trend[554] trend[555] trend[556] trend[557] trend[558]
## [1,] 0.4155522 0.4156364 0.4157206 0.4158048 0.415889 0.4159732
## trend[559] trend[560] trend[561] trend[562] trend[563] trend[564]
## [1,] 0.4160574 0.4161417 0.4162259 0.4163101 0.4163943 0.4164785
## trend[565] trend[566] trend[567] trend[568] trend[569] trend[570]
## [1,] 0.4165627 0.4166469 0.4167312 0.4168154 0.4168996 0.4169838
## trend[571] trend[572] trend[573] trend[574] trend[575] trend[576]
## [1,] 0.417068 0.4171522 0.4172364 0.4173207 0.4174049 0.4174891
## trend[577] trend[578] trend[579] trend[580] trend[581] trend[582]
## [1,] 0.4175733 0.4176575 0.4177417 0.4178259 0.4179101 0.4179944
## trend[583] trend[584] trend[585] trend[586] trend[587] trend[588]
## [1,] 0.4180786 0.4181628 0.418247 0.4183312 0.4184154 0.4184996
## trend[589] trend[590] trend[591] trend[592] trend[593] trend[594]
## [1,] 0.4185839 0.4186681 0.4187523 0.4188365 0.4189207 0.4190049
## trend[595] trend[596] trend[597] trend[598] trend[599] trend[600]
## [1,] 0.4190891 0.4191734 0.4192576 0.4193418 0.419426 0.4195102
## trend[601] trend[602] trend[603] trend[604] trend[605] trend[606]
## [1,] 0.4195944 0.4196786 0.4197629 0.4198471 0.4199313 0.4200155
## trend[607] trend[608] trend[609] trend[610] trend[611] trend[612]
## [1,] 0.4200997 0.4201839 0.4202681 0.4203523 0.4204366 0.4205208
## trend[613] trend[614] trend[615] trend[616] trend[617] trend[618]
## [1,] 0.420605 0.4206892 0.4207734 0.4208576 0.4209418 0.4210261
## trend[619] trend[620] trend[621] trend[622] trend[623] trend[624]
## [1,] 0.4211103 0.4211945 0.4212787 0.4213629 0.4214471 0.4215313
## trend[625] trend[626] trend[627] trend[628] trend[629] trend[630]
## [1,] 0.4216156 0.4216998 0.421784 0.4218682 0.4219524 0.4220366
## trend[631] trend[632] trend[633] trend[634] trend[635] trend[636]
## [1,] 0.4221208 0.4222051 0.4222893 0.4223735 0.4224577 0.4225419
## trend[637] trend[638] trend[639] trend[640] trend[641] trend[642]
## [1,] 0.4226261 0.4227103 0.4227945 0.4228788 0.422963 0.4230472
## trend[643] trend[644] trend[645] trend[646] trend[647] trend[648]
## [1,] 0.4231314 0.4232156 0.4232998 0.423384 0.4234683 0.4235525
## trend[649] trend[650] trend[651] trend[652] trend[653] trend[654]
## [1,] 0.4236367 0.4237209 0.4238051 0.4238893 0.4239735 0.4240578
## trend[655] trend[656] trend[657] trend[658] trend[659] trend[660]
## [1,] 0.424142 0.4242239 0.4243058 0.4243877 0.4244696 0.4245515
## trend[661] trend[662] trend[663] trend[664] trend[665] trend[666]
## [1,] 0.4246335 0.4247154 0.4247973 0.4248792 0.4249611 0.425043
## trend[667] trend[668] trend[669] trend[670] trend[671] trend[672]
## [1,] 0.4251249 0.4252069 0.4252888 0.4253707 0.4254526 0.4255345
## trend[673] trend[674] trend[675] trend[676] trend[677] trend[678]
## [1,] 0.4256164 0.4256983 0.4257803 0.4258622 0.4259441 0.426026
## trend[679] trend[680] trend[681] trend[682] trend[683] trend[684]
## [1,] 0.4261079 0.4261898 0.4262717 0.4263537 0.4264356 0.4265175
## trend[685] trend[686] trend[687] trend[688] trend[689] trend[690]
## [1,] 0.4265994 0.4266813 0.4267632 0.4268451 0.4269271 0.427009
## trend[691] trend[692] trend[693] trend[694] trend[695] trend[696]
## [1,] 0.4270909 0.4271728 0.4272547 0.4273366 0.4274185 0.4275005
## trend[697] trend[698] trend[699] trend[700] trend[701] trend[702]
## [1,] 0.4275824 0.4276643 0.4277462 0.4278281 0.42791 0.4279663
## trend[703] trend[704] trend[705] trend[706] trend[707] trend[708]
## [1,] 0.4280225 0.4280787 0.428135 0.4281912 0.4282474 0.4283037
## trend[709] trend[710] trend[711] trend[712] trend[713] trend[714]
## [1,] 0.4283599 0.4284161 0.4284724 0.4285286 0.4285848 0.4286411
## trend[715] trend[716] trend[717] trend[718] trend[719] trend[720]
## [1,] 0.4286973 0.4287535 0.4288098 0.428866 0.4289222 0.4289785
## trend[721] trend[722] trend[723] trend[724] trend[725] trend[726]
## [1,] 0.4290347 0.4290909 0.4291472 0.4292034 0.4292596 0.4293159
## trend[727] trend[728] trend[729] trend[730] trend[731] trend[732]
## [1,] 0.4293721 0.4294283 0.4294846 0.4295408 0.429597 0.4296533
## trend[733] trend[734] trend[735] trend[736] trend[737] trend[738]
## [1,] 0.4297095 0.4297657 0.429822 0.4298782 0.4299344 0.4299907
## trend[739] trend[740] trend[741] trend[742] trend[743] trend[744]
## [1,] 0.4300469 0.4301031 0.4301594 0.4302156 0.4302718 0.4303281
## trend[745] trend[746] trend[747] trend[748] trend[749] trend[750]
## [1,] 0.4303843 0.4304405 0.4304968 0.430553 0.4306092 0.4306655
## trend[751] trend[752] trend[753] trend[754] trend[755] trend[756]
## [1,] 0.4307217 0.4307779 0.4308342 0.4308904 0.4309466 0.4310029
## trend[757] trend[758] trend[759] trend[760] trend[761] trend[762]
## [1,] 0.4310591 0.4311153 0.4311716 0.4312278 0.431284 0.4313403
## trend[763] trend[764] trend[765] trend[766] trend[767] trend[768]
## [1,] 0.4313965 0.4314527 0.431509 0.4315652 0.4316214 0.4316777
## trend[769] trend[770] trend[771] trend[772] trend[773] trend[774]
## [1,] 0.4317339 0.4317901 0.4318464 0.4319026 0.4319588 0.4320151
## trend[775] trend[776] trend[777] trend[778] trend[779] trend[780]
## [1,] 0.4320713 0.4321275 0.4321838 0.43224 0.4322962 0.4323525
## trend[781] trend[782] trend[783] trend[784] trend[785] trend[786]
## [1,] 0.4324087 0.4324649 0.4325212 0.4325774 0.4326336 0.4326899
## trend[787] trend[788] trend[789] trend[790] trend[791] trend[792]
## [1,] 0.4327461 0.4328023 0.4328586 0.4329148 0.432971 0.4330273
## trend[793] trend[794] trend[795] trend[796] trend[797] trend[798]
## [1,] 0.4330835 0.4331397 0.433196 0.4332522 0.4333084 0.4333647
## trend[799] trend[800] trend[801] trend[802] trend[803] trend[804]
## [1,] 0.4334209 0.4334771 0.4335334 0.4335896 0.4336458 0.4337021
## trend[805] trend[806] trend[807] trend[808] trend[809] trend[810]
## [1,] 0.4337583 0.4338145 0.4338708 0.433927 0.4339832 0.4340395
## trend[811] trend[812] trend[813] trend[814] trend[815] trend[816]
## [1,] 0.4340957 0.434152 0.4342082 0.4342644 0.4343207 0.4343769
## trend[817] trend[818] trend[819] trend[820] trend[821] trend[822]
## [1,] 0.4344331 0.4344894 0.4345456 0.4346018 0.4346581 0.4347143
## trend[823] trend[824] trend[825] trend[826] trend[827] trend[828]
## [1,] 0.4347705 0.4348268 0.434883 0.4349392 0.4349955 0.4350517
## trend[829] trend[830] trend[831] trend[832] trend[833] trend[834]
## [1,] 0.4351079 0.4351642 0.4352204 0.4352766 0.4353329 0.4353891
## trend[835] trend[836] trend[837] trend[838] trend[839] trend[840]
## [1,] 0.4354453 0.4355016 0.4355578 0.435614 0.4356703 0.4357265
## trend[841] trend[842] trend[843] trend[844] trend[845] trend[846]
## [1,] 0.4357827 0.4358439 0.4359051 0.4359663 0.4360275 0.4360887
## trend[847] trend[848] trend[849] trend[850] trend[851] trend[852]
## [1,] 0.4361499 0.4362111 0.4362723 0.4363334 0.4363946 0.4364558
## trend[853] trend[854] trend[855] trend[856] trend[857] trend[858]
## [1,] 0.436517 0.4365782 0.4366394 0.4367006 0.4367618 0.436823
## trend[859] trend[860] trend[861] trend[862] trend[863] trend[864]
## [1,] 0.4368842 0.4369454 0.4370066 0.4370678 0.4371289 0.4371901
## trend[865] trend[866] trend[867] trend[868] trend[869] trend[870]
## [1,] 0.4372513 0.4373125 0.4373737 0.4374349 0.4374961 0.4375573
## trend[871] trend[872] trend[873] trend[874] trend[875] trend[876]
## [1,] 0.4376185 0.4376797 0.4377409 0.4378021 0.4378632 0.4379244
## trend[877] trend[878] trend[879] trend[880] trend[881] trend[882]
## [1,] 0.4379856 0.4380468 0.438108 0.4381692 0.4382304 0.4382916
## trend[883] trend[884] trend[885] trend[886] trend[887] trend[888]
## [1,] 0.4383528 0.438414 0.4384752 0.4385364 0.4385976 0.4386587
## trend[889] trend[890] trend[891] trend[892] trend[893] trend[894]
## [1,] 0.4387389 0.438819 0.4388992 0.4389793 0.4390595 0.4391396
## trend[895] trend[896] trend[897] trend[898] trend[899] trend[900]
## [1,] 0.4392198 0.4392999 0.4393801 0.4394602 0.4395404 0.4396205
## trend[901] trend[902] trend[903] trend[904] trend[905] trend[906]
## [1,] 0.4397007 0.4397808 0.439861 0.4399411 0.4400213 0.4401014
## trend[907] trend[908] trend[909] trend[910] trend[911] trend[912]
## [1,] 0.4401816 0.4402617 0.4403419 0.440422 0.4405022 0.4405823
## trend[913] trend[914] trend[915] trend[916] trend[917] trend[918]
## [1,] 0.4406625 0.4407426 0.4408228 0.4409029 0.440983 0.4410632
## trend[919] trend[920] trend[921] trend[922] trend[923] trend[924]
## [1,] 0.4411433 0.4412235 0.4413036 0.4413838 0.4414639 0.4415441
## trend[925] trend[926] trend[927] trend[928] trend[929] trend[930]
## [1,] 0.4416242 0.4417044 0.4417845 0.4418647 0.4419448 0.442025
## trend[931] trend[932] trend[933] trend[934] trend[935] trend[936]
## [1,] 0.4421051 0.4421853 0.4422654 0.4423456 0.4424257 0.4425327
## trend[937] trend[938] trend[939] trend[940] trend[941] trend[942]
## [1,] 0.4426397 0.4427466 0.4428536 0.4429606 0.4430676 0.4431745
## trend[943] trend[944] trend[945] trend[946] trend[947] trend[948]
## [1,] 0.4432815 0.4433885 0.4434955 0.4436024 0.4437094 0.4438164
## trend[949] trend[950] trend[951] trend[952] trend[953] trend[954]
## [1,] 0.4439234 0.4440303 0.4441373 0.4442443 0.4443513 0.4444582
## trend[955] trend[956] trend[957] trend[958] trend[959] trend[960]
## [1,] 0.4445652 0.4446722 0.4447792 0.4448861 0.4449931 0.4451001
## trend[961] trend[962] trend[963] trend[964] trend[965] trend[966]
## [1,] 0.4452071 0.445314 0.445421 0.445528 0.445635 0.4457419
## trend[967] trend[968] trend[969] trend[970] trend[971] trend[972]
## [1,] 0.4458489 0.4459559 0.4460629 0.4461698 0.4462768 0.4463838
## trend[973] trend[974] trend[975] trend[976] trend[977] trend[978]
## [1,] 0.4464908 0.4465977 0.4467047 0.4468117 0.4469187 0.4470256
## trend[979] trend[980] trend[981] trend[982] trend[983] trend[984]
## [1,] 0.4471326 0.4472396 0.4473466 0.4475024 0.4476581 0.4478139
## trend[985] trend[986] trend[987] trend[988] trend[989] trend[990]
## [1,] 0.4479697 0.4481255 0.4482813 0.4484371 0.4485929 0.4487487
## trend[991] trend[992] trend[993] trend[994] trend[995] trend[996]
## [1,] 0.4489045 0.4490602 0.449216 0.4493718 0.4495276 0.4496834
## trend[997] trend[998] trend[999] trend[1000] trend[1001] trend[1002]
## [1,] 0.4498392 0.449995 0.4501508 0.4503065 0.4504623 0.4506181
## trend[1003] trend[1004] trend[1005] trend[1006] trend[1007] trend[1008]
## [1,] 0.4507739 0.4509297 0.4510855 0.4512413 0.4513971 0.4515528
## trend[1009] trend[1010] trend[1011] trend[1012] trend[1013] trend[1014]
## [1,] 0.4517086 0.4518644 0.4520202 0.452176 0.4523318 0.4524876
## trend[1015] trend[1016] trend[1017] trend[1018] trend[1019] trend[1020]
## [1,] 0.4526434 0.4527992 0.4529549 0.4531107 0.4532665 0.4534223
## trend[1021] trend[1022] trend[1023] trend[1024] trend[1025] trend[1026]
## [1,] 0.4535781 0.4537339 0.4538897 0.4540455 0.4542012 0.454357
## trend[1027] trend[1028] trend[1029] trend[1030] trend[1031] trend[1032]
## [1,] 0.4545128 0.4546686 0.454836 0.4550033 0.4551706 0.455338
## trend[1033] trend[1034] trend[1035] trend[1036] trend[1037] trend[1038]
## [1,] 0.4555053 0.4556727 0.45584 0.4560074 0.4561747 0.4563421
## trend[1039] trend[1040] trend[1041] trend[1042] trend[1043] trend[1044]
## [1,] 0.4565094 0.4566768 0.4568441 0.4570114 0.4571788 0.4573461
## trend[1045] trend[1046] trend[1047] trend[1048] trend[1049] trend[1050]
## [1,] 0.4575135 0.4576808 0.4578482 0.4580155 0.4581829 0.4583502
## trend[1051] trend[1052] trend[1053] trend[1054] trend[1055] trend[1056]
## [1,] 0.4585176 0.4586849 0.4588523 0.4590196 0.4591869 0.4593543
## trend[1057] trend[1058] trend[1059] trend[1060] trend[1061] trend[1062]
## [1,] 0.4595216 0.459689 0.4598563 0.4600237 0.460191 0.4603584
## trend[1063] trend[1064] trend[1065] trend[1066] trend[1067] trend[1068]
## [1,] 0.4605257 0.4606931 0.4608604 0.4610277 0.4611951 0.4613624
## trend[1069] trend[1070] trend[1071] trend[1072] trend[1073] trend[1074]
## [1,] 0.4615298 0.4616971 0.4618645 0.4620318 0.4621992 0.4623665
## trend[1075] trend[1076] trend[1077] trend[1078] trend[1079] trend[1080]
## [1,] 0.4625339 0.4627039 0.4628739 0.4630439 0.4632139 0.4633839
## trend[1081] trend[1082] trend[1083] trend[1084] trend[1085] trend[1086]
## [1,] 0.4635539 0.4637239 0.4638939 0.4640639 0.464234 0.464404
## trend[1087] trend[1088] trend[1089] trend[1090] trend[1091] trend[1092]
## [1,] 0.464574 0.464744 0.464914 0.465084 0.465254 0.465424
## trend[1093] trend[1094] trend[1095] trend[1096] trend[1097] trend[1098]
## [1,] 0.465594 0.465764 0.465934 0.4661041 0.4662741 0.4664441
## trend[1099] trend[1100] trend[1101] trend[1102] trend[1103] trend[1104]
## [1,] 0.4666141 0.4667841 0.4669541 0.4671241 0.4672941 0.4674641
## trend[1105] trend[1106] trend[1107] trend[1108] trend[1109] trend[1110]
## [1,] 0.4676341 0.4678042 0.4679742 0.4681442 0.4683142 0.4684842
## trend[1111] trend[1112] trend[1113] trend[1114] trend[1115] trend[1116]
## [1,] 0.4686542 0.4688242 0.4689942 0.4691642 0.4693342 0.4695042
## trend[1117] trend[1118] trend[1119] trend[1120] trend[1121] trend[1122]
## [1,] 0.4696743 0.4698443 0.4700143 0.4701843 0.4703543 0.4705243
## trend[1123] trend[1124] trend[1125] trend[1126] trend[1127] trend[1128]
## [1,] 0.4706943 0.4708643 0.4710343 0.4712043 0.4713743 0.4715444
## trend[1129] trend[1130] trend[1131] trend[1132] trend[1133] trend[1134]
## [1,] 0.4717144 0.4718844 0.4720544 0.4722244 0.4723944 0.4725644
## trend[1135] trend[1136] trend[1137] trend[1138] trend[1139] trend[1140]
## [1,] 0.4727344 0.4729044 0.4730744 0.4732444 0.4734145 0.4735845
## trend[1141] trend[1142] trend[1143] trend[1144] trend[1145] trend[1146]
## [1,] 0.4737545 0.4739245 0.4740945 0.4742645 0.4744345 0.4746045
## trend[1147] trend[1148] trend[1149] trend[1150] trend[1151] trend[1152]
## [1,] 0.4747745 0.4749445 0.4751146 0.4752846 0.4754546 0.4756246
## trend[1153] trend[1154] trend[1155] trend[1156] trend[1157] trend[1158]
## [1,] 0.4757946 0.4759646 0.4761346 0.4763046 0.4764746 0.4766446
## trend[1159] trend[1160] trend[1161] trend[1162] trend[1163] trend[1164]
## [1,] 0.4768146 0.4769847 0.4771547 0.4773247 0.4774947 0.4776647
## trend[1165] trend[1166] trend[1167] trend[1168] trend[1169] trend[1170]
## [1,] 0.4778347 0.4780047 0.4781747 0.4783447 0.4784675 0.4785903
## trend[1171] trend[1172] trend[1173] trend[1174] trend[1175] trend[1176]
## [1,] 0.4787131 0.4788359 0.4789587 0.4790815 0.4792043 0.479327
## trend[1177] trend[1178] trend[1179] trend[1180] trend[1181] trend[1182]
## [1,] 0.4794498 0.4795726 0.4796954 0.4798182 0.479941 0.4800638
## trend[1183] trend[1184] trend[1185] trend[1186] trend[1187] trend[1188]
## [1,] 0.4801866 0.4803094 0.4804321 0.4805549 0.4806777 0.4808005
## trend[1189] trend[1190] trend[1191] trend[1192] trend[1193] trend[1194]
## [1,] 0.4809233 0.4810461 0.4811689 0.4812917 0.4814145 0.4815372
## trend[1195] trend[1196] trend[1197] trend[1198] trend[1199] trend[1200]
## [1,] 0.48166 0.4817828 0.4819056 0.4820284 0.4821512 0.482274
## trend[1201] trend[1202] trend[1203] trend[1204] trend[1205] trend[1206]
## [1,] 0.4823968 0.4825195 0.4826423 0.4827651 0.4828879 0.4830107
## trend[1207] trend[1208] trend[1209] trend[1210] trend[1211] trend[1212]
## [1,] 0.4831335 0.4832563 0.4833791 0.4835019 0.4836246 0.4837474
## trend[1213] trend[1214] trend[1215] trend[1216] trend[1217] trend[1218]
## [1,] 0.4838702 0.483993 0.4841158 0.4842386 0.4843614 0.4844842
## trend[1219] trend[1220] trend[1221] trend[1222] trend[1223] trend[1224]
## [1,] 0.484607 0.4847297 0.4848525 0.4849753 0.4850981 0.4852209
## trend[1225] trend[1226] trend[1227] trend[1228] trend[1229] trend[1230]
## [1,] 0.4853437 0.4854665 0.4855893 0.4857121 0.4858348 0.4859576
## trend[1231] trend[1232] trend[1233] trend[1234] trend[1235] trend[1236]
## [1,] 0.4860804 0.4862032 0.486326 0.4864488 0.4865716 0.4866944
## trend[1237] trend[1238] trend[1239] trend[1240] trend[1241] trend[1242]
## [1,] 0.4868172 0.4869399 0.4870627 0.4871855 0.4873083 0.4874311
## trend[1243] trend[1244] trend[1245] trend[1246] trend[1247] trend[1248]
## [1,] 0.4875539 0.4876767 0.4877995 0.4879223 0.488045 0.4881678
## trend[1249] trend[1250] trend[1251] trend[1252] trend[1253] trend[1254]
## [1,] 0.4882906 0.4884134 0.4885362 0.488659 0.4887818 0.4889046
## trend[1255] trend[1256] trend[1257] trend[1258] trend[1259] trend[1260]
## [1,] 0.4890274 0.4891501 0.4892729 0.4893957 0.4895185 0.4896413
## trend[1261] trend[1262] trend[1263] trend[1264] trend[1265] trend[1266]
## [1,] 0.4897641 0.4898869 0.4900097 0.4901325 0.4902552 0.490378
## trend[1267] trend[1268] trend[1269] trend[1270] trend[1271] trend[1272]
## [1,] 0.4905008 0.4906236 0.4907464 0.4908692 0.490992 0.4911148
## trend[1273] trend[1274] trend[1275] trend[1276] trend[1277] trend[1278]
## [1,] 0.4912376 0.4913603 0.4914831 0.4916059 0.4917287 0.4918515
## trend[1279] trend[1280] trend[1281] trend[1282] trend[1283] trend[1284]
## [1,] 0.4919743 0.4920971 0.4922199 0.4923427 0.4924654 0.4925882
## trend[1285] trend[1286] trend[1287] trend[1288] trend[1289] trend[1290]
## [1,] 0.492711 0.4928338 0.4929566 0.4930794 0.4932022 0.493325
## trend[1291] trend[1292] trend[1293] trend[1294] trend[1295] trend[1296]
## [1,] 0.4934478 0.4935705 0.4936933 0.4938161 0.4939389 0.4940617
## trend[1297] trend[1298] trend[1299] trend[1300] trend[1301] trend[1302]
## [1,] 0.4941845 0.4943073 0.4944301 0.4945529 0.4946756 0.4947984
## trend[1303] trend[1304] trend[1305] trend[1306] trend[1307] trend[1308]
## [1,] 0.4949212 0.495044 0.4951668 0.4952896 0.4954124 0.4955352
## trend[1309] trend[1310] trend[1311] trend[1312] trend[1313] trend[1314]
## [1,] 0.495658 0.4957807 0.4959035 0.4960263 0.4961491 0.4962719
## trend[1315] trend[1316] trend[1317] trend[1318] trend[1319] trend[1320]
## [1,] 0.4963947 0.4965175 0.4966403 0.496763 0.4968858 0.4970086
## trend[1321] trend[1322] trend[1323] trend[1324] trend[1325] trend[1326]
## [1,] 0.4971314 0.4972542 0.497377 0.4974998 0.4976226 0.4977454
## trend[1327] trend[1328] trend[1329] trend[1330] trend[1331] trend[1332]
## [1,] 0.4978681 0.4979909 0.4981137 0.4982365 0.4983593 0.4984821
## trend[1333] trend[1334] trend[1335] trend[1336] trend[1337] trend[1338]
## [1,] 0.4986049 0.4987277 0.4988505 0.4989732 0.499096 0.4992188
## trend[1339] trend[1340] trend[1341] trend[1342] trend[1343] trend[1344]
## [1,] 0.4993416 0.4994644 0.4995872 0.49971 0.4998328 0.4999556
## trend[1345] trend[1346] trend[1347] trend[1348] trend[1349] trend[1350]
## [1,] 0.5000783 0.5002011 0.5003239 0.5004467 0.5005695 0.5006923
## trend[1351] trend[1352] trend[1353] trend[1354] trend[1355] trend[1356]
## [1,] 0.5008151 0.5009379 0.5010607 0.5011834 0.5013062 0.501429
## trend[1357] trend[1358] trend[1359] trend[1360] trend[1361] trend[1362]
## [1,] 0.5015518 0.5016746 0.5017974 0.5019202 0.502043 0.5021658
## trend[1363] trend[1364] trend[1365] trend[1366] trend[1367] trend[1368]
## [1,] 0.5022885 0.5024113 0.5025341 0.5026569 0.5027797 0.5029025
## trend[1369] trend[1370] trend[1371] trend[1372] trend[1373] trend[1374]
## [1,] 0.5030253 0.5031481 0.5032709 0.5033936 0.5035164 0.5036392
## trend[1375] trend[1376] trend[1377] trend[1378] trend[1379] trend[1380]
## [1,] 0.503762 0.5038848 0.5040076 0.5041304 0.5042532 0.504376
## trend[1381] trend[1382] trend[1383] trend[1384] trend[1385] trend[1386]
## [1,] 0.5044987 0.5046215 0.5047443 0.5048671 0.5049899 0.5051127
## trend[1387] trend[1388] trend[1389] trend[1390] trend[1391] trend[1392]
## [1,] 0.5052355 0.5053583 0.5054811 0.5056038 0.5057266 0.5058494
## trend[1393] trend[1394] trend[1395] trend[1396] trend[1397] trend[1398]
## [1,] 0.5059722 0.506095 0.5062178 0.5063406 0.5064634 0.5065862
## trend[1399] trend[1400] trend[1401] trend[1402] trend[1403] trend[1404]
## [1,] 0.5067089 0.5068317 0.5069545 0.5070773 0.5072001 0.5073229
## trend[1405] trend[1406] trend[1407] trend[1408] trend[1409] trend[1410]
## [1,] 0.5074457 0.5075685 0.5076913 0.507814 0.5079368 0.5080596
## trend[1411] trend[1412] trend[1413] trend[1414] trend[1415] trend[1416]
## [1,] 0.5081824 0.5083052 0.508428 0.5085508 0.5086736 0.5087964
## trend[1417] trend[1418] trend[1419] trend[1420] trend[1421] trend[1422]
## [1,] 0.5089191 0.5090419 0.5091647 0.5092875 0.5094103 0.5095331
## trend[1423] trend[1424] trend[1425] trend[1426] trend[1427] trend[1428]
## [1,] 0.5096559 0.5097787 0.5099015 0.5100242 0.510147 0.5102698
## trend[1429] trend[1430] trend[1431] trend[1432] trend[1433] trend[1434]
## [1,] 0.5103926 0.5105154 0.5106382 0.510761 0.5108838 0.5110065
## trend[1435] trend[1436] trend[1437] trend[1438] trend[1439] trend[1440]
## [1,] 0.5111293 0.5112521 0.5113749 0.5114977 0.5116205 0.5117433
## trend[1441] trend[1442] trend[1443] trend[1444] trend[1445] trend[1446]
## [1,] 0.5118661 0.5119889 0.5121116 0.5122344 0.5123572 0.51248
## trend[1447] trend[1448] trend[1449] trend[1450] trend[1451] trend[1452]
## [1,] 0.5126028 0.5127256 0.5128484 0.5129712 0.513094 0.5132167
## trend[1453] trend[1454] trend[1455] trend[1456] trend[1457] trend[1458]
## [1,] 0.5133395 0.5134623 0.5135851 0.5137079 0.5138307 0.5139535
## trend[1459] trend[1460] trend[1461]
## [1,] 0.5140763 0.5141991 0.5143218
##
##
## $params
## $params$k
## [1] -0.3399185
##
## $params$m
## [1] 0.3551693
##
## $params$delta
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 7.557253e-08 3.483415e-08 0.268866 0.4799589 0.2004927 6.476051e-08
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 5.903609e-08 -0.2108516 -0.2755958 -1.215397e-07 4.155e-08 2.488461e-07
## [,13] [,14] [,15] [,16] [,17]
## [1,] -1.266203e-08 -0.003357057 -0.03749413 -1.522682e-08 -6.884554e-08
## [,18] [,19] [,20] [,21] [,22] [,23]
## [1,] 0.007239539 0.02767627 0.03916694 0.0712668 0.01687457 0.003888608
## [,24] [,25]
## [1,] 1.302859e-07 -0.06894206
##
## $params$sigma_obs
## [1] 0.02704036
##
## $params$beta
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.01503878 -0.1395354 -0.02416547 -0.007901517 -0.01777479 -0.02432104
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.007693029 -0.008147217 0.006676297 -0.0118898 0.01535229 0.003032079
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 0.003252465 0.009647003 0.004167203 0.005074982 -0.007422047 0.00594854
## [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] -0.004875237 -0.0004564492 0.07696883 -0.00257081 -0.04462161 -0.009995736
## [,25] [,26] [,27] [,28] [,29] [,30]
## [1,] 0.04729456 0.006687925 -5.405959e-11 0.0382359 -1.081192e-10 0.0382359
## [,31] [,32] [,33] [,34]
## [1,] -2.690668e-11 0.0382359 -2.162384e-10 0.0382359
##
## $params$trend
## [1] 0.3551693 0.3549365 0.3547037 0.3544709 0.3542380 0.3540052 0.3537724
## [8] 0.3535396 0.3533068 0.3530739 0.3528411 0.3526083 0.3523755 0.3521427
## [15] 0.3519098 0.3516770 0.3514442 0.3512114 0.3509785 0.3507457 0.3505129
## [22] 0.3502801 0.3500473 0.3498144 0.3495816 0.3493488 0.3491160 0.3488832
## [29] 0.3486503 0.3484175 0.3481847 0.3479519 0.3477191 0.3474862 0.3472534
## [36] 0.3470206 0.3467878 0.3465550 0.3463221 0.3460893 0.3458565 0.3456237
## [43] 0.3453908 0.3451580 0.3449252 0.3446924 0.3444596 0.3442267 0.3439939
## [50] 0.3437611 0.3435283 0.3432955 0.3430626 0.3428298 0.3425970 0.3423642
## [57] 0.3421314 0.3418985 0.3416657 0.3414329 0.3412001 0.3409673 0.3407344
## [64] 0.3405016 0.3402688 0.3400360 0.3398031 0.3395703 0.3393375 0.3391047
## [71] 0.3388719 0.3386390 0.3384062 0.3381734 0.3379406 0.3377078 0.3374749
## [78] 0.3372421 0.3370093 0.3367765 0.3365437 0.3363108 0.3360780 0.3358452
## [85] 0.3356124 0.3353796 0.3351467 0.3349139 0.3346811 0.3344483 0.3342154
## [92] 0.3339826 0.3337498 0.3335170 0.3332842 0.3330513 0.3328185 0.3325857
## [99] 0.3323529 0.3321201 0.3318872 0.3316544 0.3314216 0.3311888 0.3309560
## [106] 0.3307231 0.3304903 0.3302575 0.3300247 0.3297919 0.3295590 0.3293262
## [113] 0.3290934 0.3288606 0.3286277 0.3283949 0.3281621 0.3279293 0.3276965
## [120] 0.3274636 0.3272308 0.3269980 0.3267652 0.3265324 0.3262995 0.3260667
## [127] 0.3258339 0.3256011 0.3253683 0.3251354 0.3249026 0.3246698 0.3244370
## [134] 0.3242042 0.3239713 0.3237385 0.3235057 0.3232729 0.3230400 0.3228072
## [141] 0.3225744 0.3225257 0.3224771 0.3224284 0.3223797 0.3223311 0.3222824
## [148] 0.3222337 0.3221851 0.3221364 0.3220877 0.3220391 0.3219904 0.3219417
## [155] 0.3218931 0.3218444 0.3217957 0.3217471 0.3216984 0.3216498 0.3216011
## [162] 0.3215524 0.3215038 0.3214551 0.3214064 0.3213578 0.3213091 0.3212604
## [169] 0.3212118 0.3211631 0.3211144 0.3210658 0.3210171 0.3209684 0.3209198
## [176] 0.3208711 0.3208224 0.3207738 0.3207251 0.3206764 0.3206278 0.3205791
## [183] 0.3205304 0.3204818 0.3204331 0.3203844 0.3203358 0.3202871 0.3205672
## [190] 0.3208472 0.3211273 0.3214074 0.3216875 0.3219675 0.3222476 0.3225277
## [197] 0.3228078 0.3230878 0.3233679 0.3236480 0.3239280 0.3242081 0.3244882
## [204] 0.3247683 0.3250483 0.3253284 0.3256085 0.3258886 0.3261686 0.3264487
## [211] 0.3267288 0.3270089 0.3272889 0.3275690 0.3278491 0.3281291 0.3284092
## [218] 0.3286893 0.3289694 0.3292494 0.3295295 0.3298096 0.3300897 0.3303697
## [225] 0.3306498 0.3309299 0.3312099 0.3314900 0.3317701 0.3320502 0.3323302
## [232] 0.3326103 0.3328904 0.3331705 0.3335879 0.3340052 0.3344226 0.3348400
## [239] 0.3352574 0.3356748 0.3360922 0.3365096 0.3369270 0.3373444 0.3377618
## [246] 0.3381792 0.3385966 0.3390140 0.3394314 0.3398488 0.3402662 0.3406836
## [253] 0.3411010 0.3415184 0.3419358 0.3423532 0.3427706 0.3431880 0.3436054
## [260] 0.3440228 0.3444402 0.3448576 0.3452750 0.3456924 0.3461098 0.3465272
## [267] 0.3469445 0.3473619 0.3477793 0.3481967 0.3486141 0.3490315 0.3494489
## [274] 0.3498663 0.3502837 0.3507011 0.3511185 0.3515359 0.3519533 0.3523707
## [281] 0.3527881 0.3532055 0.3536229 0.3540403 0.3544577 0.3548751 0.3552925
## [288] 0.3557099 0.3561273 0.3565447 0.3569621 0.3573795 0.3577969 0.3582143
## [295] 0.3586317 0.3590491 0.3594665 0.3598838 0.3603012 0.3607186 0.3611360
## [302] 0.3615534 0.3619708 0.3623882 0.3628056 0.3632230 0.3636404 0.3640578
## [309] 0.3644752 0.3648926 0.3653100 0.3657274 0.3661448 0.3665622 0.3669796
## [316] 0.3673970 0.3678144 0.3682318 0.3686492 0.3690666 0.3694840 0.3699014
## [323] 0.3703188 0.3707362 0.3711536 0.3715710 0.3719884 0.3724057 0.3728231
## [330] 0.3732405 0.3736579 0.3740753 0.3744927 0.3749101 0.3753275 0.3757449
## [337] 0.3761623 0.3765797 0.3769971 0.3774145 0.3778319 0.3782493 0.3786667
## [344] 0.3790841 0.3795015 0.3799189 0.3803363 0.3807537 0.3811711 0.3815885
## [351] 0.3820059 0.3824233 0.3828407 0.3832581 0.3836755 0.3840929 0.3845103
## [358] 0.3849277 0.3853451 0.3857624 0.3861798 0.3865972 0.3870146 0.3874320
## [365] 0.3878494 0.3882668 0.3886842 0.3891016 0.3895190 0.3899364 0.3903538
## [372] 0.3907712 0.3911886 0.3916060 0.3918790 0.3921520 0.3924249 0.3926979
## [379] 0.3929709 0.3932439 0.3935168 0.3937898 0.3940628 0.3943358 0.3946088
## [386] 0.3948817 0.3951547 0.3954277 0.3957007 0.3959736 0.3962466 0.3965196
## [393] 0.3967926 0.3970656 0.3973385 0.3976115 0.3978845 0.3981575 0.3984305
## [400] 0.3987034 0.3989764 0.3992494 0.3995224 0.3997953 0.4000683 0.4003413
## [407] 0.4006143 0.4008873 0.4011602 0.4014332 0.4017062 0.4019792 0.4022521
## [414] 0.4025251 0.4027981 0.4030711 0.4033441 0.4036170 0.4038900 0.4041630
## [421] 0.4044360 0.4045202 0.4046044 0.4046886 0.4047728 0.4048570 0.4049412
## [428] 0.4050255 0.4051097 0.4051939 0.4052781 0.4053623 0.4054465 0.4055307
## [435] 0.4056150 0.4056992 0.4057834 0.4058676 0.4059518 0.4060360 0.4061202
## [442] 0.4062045 0.4062887 0.4063729 0.4064571 0.4065413 0.4066255 0.4067097
## [449] 0.4067939 0.4068782 0.4069624 0.4070466 0.4071308 0.4072150 0.4072992
## [456] 0.4073834 0.4074677 0.4075519 0.4076361 0.4077203 0.4078045 0.4078887
## [463] 0.4079729 0.4080572 0.4081414 0.4082256 0.4083098 0.4083940 0.4084782
## [470] 0.4085624 0.4086466 0.4087309 0.4088151 0.4088993 0.4089835 0.4090677
## [477] 0.4091519 0.4092361 0.4093204 0.4094046 0.4094888 0.4095730 0.4096572
## [484] 0.4097414 0.4098256 0.4099099 0.4099941 0.4100783 0.4101625 0.4102467
## [491] 0.4103309 0.4104151 0.4104993 0.4105836 0.4106678 0.4107520 0.4108362
## [498] 0.4109204 0.4110046 0.4110888 0.4111731 0.4112573 0.4113415 0.4114257
## [505] 0.4115099 0.4115941 0.4116783 0.4117626 0.4118468 0.4119310 0.4120152
## [512] 0.4120994 0.4121836 0.4122678 0.4123520 0.4124363 0.4125205 0.4126047
## [519] 0.4126889 0.4127731 0.4128573 0.4129415 0.4130258 0.4131100 0.4131942
## [526] 0.4132784 0.4133626 0.4134468 0.4135310 0.4136153 0.4136995 0.4137837
## [533] 0.4138679 0.4139521 0.4140363 0.4141205 0.4142047 0.4142890 0.4143732
## [540] 0.4144574 0.4145416 0.4146258 0.4147100 0.4147942 0.4148785 0.4149627
## [547] 0.4150469 0.4151311 0.4152153 0.4152995 0.4153837 0.4154679 0.4155522
## [554] 0.4156364 0.4157206 0.4158048 0.4158890 0.4159732 0.4160574 0.4161417
## [561] 0.4162259 0.4163101 0.4163943 0.4164785 0.4165627 0.4166469 0.4167312
## [568] 0.4168154 0.4168996 0.4169838 0.4170680 0.4171522 0.4172364 0.4173207
## [575] 0.4174049 0.4174891 0.4175733 0.4176575 0.4177417 0.4178259 0.4179101
## [582] 0.4179944 0.4180786 0.4181628 0.4182470 0.4183312 0.4184154 0.4184996
## [589] 0.4185839 0.4186681 0.4187523 0.4188365 0.4189207 0.4190049 0.4190891
## [596] 0.4191734 0.4192576 0.4193418 0.4194260 0.4195102 0.4195944 0.4196786
## [603] 0.4197629 0.4198471 0.4199313 0.4200155 0.4200997 0.4201839 0.4202681
## [610] 0.4203523 0.4204366 0.4205208 0.4206050 0.4206892 0.4207734 0.4208576
## [617] 0.4209418 0.4210261 0.4211103 0.4211945 0.4212787 0.4213629 0.4214471
## [624] 0.4215313 0.4216156 0.4216998 0.4217840 0.4218682 0.4219524 0.4220366
## [631] 0.4221208 0.4222051 0.4222893 0.4223735 0.4224577 0.4225419 0.4226261
## [638] 0.4227103 0.4227945 0.4228788 0.4229630 0.4230472 0.4231314 0.4232156
## [645] 0.4232998 0.4233840 0.4234683 0.4235525 0.4236367 0.4237209 0.4238051
## [652] 0.4238893 0.4239735 0.4240578 0.4241420 0.4242239 0.4243058 0.4243877
## [659] 0.4244696 0.4245515 0.4246335 0.4247154 0.4247973 0.4248792 0.4249611
## [666] 0.4250430 0.4251249 0.4252069 0.4252888 0.4253707 0.4254526 0.4255345
## [673] 0.4256164 0.4256983 0.4257803 0.4258622 0.4259441 0.4260260 0.4261079
## [680] 0.4261898 0.4262717 0.4263537 0.4264356 0.4265175 0.4265994 0.4266813
## [687] 0.4267632 0.4268451 0.4269271 0.4270090 0.4270909 0.4271728 0.4272547
## [694] 0.4273366 0.4274185 0.4275005 0.4275824 0.4276643 0.4277462 0.4278281
## [701] 0.4279100 0.4279663 0.4280225 0.4280787 0.4281350 0.4281912 0.4282474
## [708] 0.4283037 0.4283599 0.4284161 0.4284724 0.4285286 0.4285848 0.4286411
## [715] 0.4286973 0.4287535 0.4288098 0.4288660 0.4289222 0.4289785 0.4290347
## [722] 0.4290909 0.4291472 0.4292034 0.4292596 0.4293159 0.4293721 0.4294283
## [729] 0.4294846 0.4295408 0.4295970 0.4296533 0.4297095 0.4297657 0.4298220
## [736] 0.4298782 0.4299344 0.4299907 0.4300469 0.4301031 0.4301594 0.4302156
## [743] 0.4302718 0.4303281 0.4303843 0.4304405 0.4304968 0.4305530 0.4306092
## [750] 0.4306655 0.4307217 0.4307779 0.4308342 0.4308904 0.4309466 0.4310029
## [757] 0.4310591 0.4311153 0.4311716 0.4312278 0.4312840 0.4313403 0.4313965
## [764] 0.4314527 0.4315090 0.4315652 0.4316214 0.4316777 0.4317339 0.4317901
## [771] 0.4318464 0.4319026 0.4319588 0.4320151 0.4320713 0.4321275 0.4321838
## [778] 0.4322400 0.4322962 0.4323525 0.4324087 0.4324649 0.4325212 0.4325774
## [785] 0.4326336 0.4326899 0.4327461 0.4328023 0.4328586 0.4329148 0.4329710
## [792] 0.4330273 0.4330835 0.4331397 0.4331960 0.4332522 0.4333084 0.4333647
## [799] 0.4334209 0.4334771 0.4335334 0.4335896 0.4336458 0.4337021 0.4337583
## [806] 0.4338145 0.4338708 0.4339270 0.4339832 0.4340395 0.4340957 0.4341520
## [813] 0.4342082 0.4342644 0.4343207 0.4343769 0.4344331 0.4344894 0.4345456
## [820] 0.4346018 0.4346581 0.4347143 0.4347705 0.4348268 0.4348830 0.4349392
## [827] 0.4349955 0.4350517 0.4351079 0.4351642 0.4352204 0.4352766 0.4353329
## [834] 0.4353891 0.4354453 0.4355016 0.4355578 0.4356140 0.4356703 0.4357265
## [841] 0.4357827 0.4358439 0.4359051 0.4359663 0.4360275 0.4360887 0.4361499
## [848] 0.4362111 0.4362723 0.4363334 0.4363946 0.4364558 0.4365170 0.4365782
## [855] 0.4366394 0.4367006 0.4367618 0.4368230 0.4368842 0.4369454 0.4370066
## [862] 0.4370678 0.4371289 0.4371901 0.4372513 0.4373125 0.4373737 0.4374349
## [869] 0.4374961 0.4375573 0.4376185 0.4376797 0.4377409 0.4378021 0.4378632
## [876] 0.4379244 0.4379856 0.4380468 0.4381080 0.4381692 0.4382304 0.4382916
## [883] 0.4383528 0.4384140 0.4384752 0.4385364 0.4385976 0.4386587 0.4387389
## [890] 0.4388190 0.4388992 0.4389793 0.4390595 0.4391396 0.4392198 0.4392999
## [897] 0.4393801 0.4394602 0.4395404 0.4396205 0.4397007 0.4397808 0.4398610
## [904] 0.4399411 0.4400213 0.4401014 0.4401816 0.4402617 0.4403419 0.4404220
## [911] 0.4405022 0.4405823 0.4406625 0.4407426 0.4408228 0.4409029 0.4409830
## [918] 0.4410632 0.4411433 0.4412235 0.4413036 0.4413838 0.4414639 0.4415441
## [925] 0.4416242 0.4417044 0.4417845 0.4418647 0.4419448 0.4420250 0.4421051
## [932] 0.4421853 0.4422654 0.4423456 0.4424257 0.4425327 0.4426397 0.4427466
## [939] 0.4428536 0.4429606 0.4430676 0.4431745 0.4432815 0.4433885 0.4434955
## [946] 0.4436024 0.4437094 0.4438164 0.4439234 0.4440303 0.4441373 0.4442443
## [953] 0.4443513 0.4444582 0.4445652 0.4446722 0.4447792 0.4448861 0.4449931
## [960] 0.4451001 0.4452071 0.4453140 0.4454210 0.4455280 0.4456350 0.4457419
## [967] 0.4458489 0.4459559 0.4460629 0.4461698 0.4462768 0.4463838 0.4464908
## [974] 0.4465977 0.4467047 0.4468117 0.4469187 0.4470256 0.4471326 0.4472396
## [981] 0.4473466 0.4475024 0.4476581 0.4478139 0.4479697 0.4481255 0.4482813
## [988] 0.4484371 0.4485929 0.4487487 0.4489045 0.4490602 0.4492160 0.4493718
## [995] 0.4495276 0.4496834 0.4498392 0.4499950 0.4501508 0.4503065 0.4504623
## [1002] 0.4506181 0.4507739 0.4509297 0.4510855 0.4512413 0.4513971 0.4515528
## [1009] 0.4517086 0.4518644 0.4520202 0.4521760 0.4523318 0.4524876 0.4526434
## [1016] 0.4527992 0.4529549 0.4531107 0.4532665 0.4534223 0.4535781 0.4537339
## [1023] 0.4538897 0.4540455 0.4542012 0.4543570 0.4545128 0.4546686 0.4548360
## [1030] 0.4550033 0.4551706 0.4553380 0.4555053 0.4556727 0.4558400 0.4560074
## [1037] 0.4561747 0.4563421 0.4565094 0.4566768 0.4568441 0.4570114 0.4571788
## [1044] 0.4573461 0.4575135 0.4576808 0.4578482 0.4580155 0.4581829 0.4583502
## [1051] 0.4585176 0.4586849 0.4588523 0.4590196 0.4591869 0.4593543 0.4595216
## [1058] 0.4596890 0.4598563 0.4600237 0.4601910 0.4603584 0.4605257 0.4606931
## [1065] 0.4608604 0.4610277 0.4611951 0.4613624 0.4615298 0.4616971 0.4618645
## [1072] 0.4620318 0.4621992 0.4623665 0.4625339 0.4627039 0.4628739 0.4630439
## [1079] 0.4632139 0.4633839 0.4635539 0.4637239 0.4638939 0.4640639 0.4642340
## [1086] 0.4644040 0.4645740 0.4647440 0.4649140 0.4650840 0.4652540 0.4654240
## [1093] 0.4655940 0.4657640 0.4659340 0.4661041 0.4662741 0.4664441 0.4666141
## [1100] 0.4667841 0.4669541 0.4671241 0.4672941 0.4674641 0.4676341 0.4678042
## [1107] 0.4679742 0.4681442 0.4683142 0.4684842 0.4686542 0.4688242 0.4689942
## [1114] 0.4691642 0.4693342 0.4695042 0.4696743 0.4698443 0.4700143 0.4701843
## [1121] 0.4703543 0.4705243 0.4706943 0.4708643 0.4710343 0.4712043 0.4713743
## [1128] 0.4715444 0.4717144 0.4718844 0.4720544 0.4722244 0.4723944 0.4725644
## [1135] 0.4727344 0.4729044 0.4730744 0.4732444 0.4734145 0.4735845 0.4737545
## [1142] 0.4739245 0.4740945 0.4742645 0.4744345 0.4746045 0.4747745 0.4749445
## [1149] 0.4751146 0.4752846 0.4754546 0.4756246 0.4757946 0.4759646 0.4761346
## [1156] 0.4763046 0.4764746 0.4766446 0.4768146 0.4769847 0.4771547 0.4773247
## [1163] 0.4774947 0.4776647 0.4778347 0.4780047 0.4781747 0.4783447 0.4784675
## [1170] 0.4785903 0.4787131 0.4788359 0.4789587 0.4790815 0.4792043 0.4793270
## [1177] 0.4794498 0.4795726 0.4796954 0.4798182 0.4799410 0.4800638 0.4801866
## [1184] 0.4803094 0.4804321 0.4805549 0.4806777 0.4808005 0.4809233 0.4810461
## [1191] 0.4811689 0.4812917 0.4814145 0.4815372 0.4816600 0.4817828 0.4819056
## [1198] 0.4820284 0.4821512 0.4822740 0.4823968 0.4825195 0.4826423 0.4827651
## [1205] 0.4828879 0.4830107 0.4831335 0.4832563 0.4833791 0.4835019 0.4836246
## [1212] 0.4837474 0.4838702 0.4839930 0.4841158 0.4842386 0.4843614 0.4844842
## [1219] 0.4846070 0.4847297 0.4848525 0.4849753 0.4850981 0.4852209 0.4853437
## [1226] 0.4854665 0.4855893 0.4857121 0.4858348 0.4859576 0.4860804 0.4862032
## [1233] 0.4863260 0.4864488 0.4865716 0.4866944 0.4868172 0.4869399 0.4870627
## [1240] 0.4871855 0.4873083 0.4874311 0.4875539 0.4876767 0.4877995 0.4879223
## [1247] 0.4880450 0.4881678 0.4882906 0.4884134 0.4885362 0.4886590 0.4887818
## [1254] 0.4889046 0.4890274 0.4891501 0.4892729 0.4893957 0.4895185 0.4896413
## [1261] 0.4897641 0.4898869 0.4900097 0.4901325 0.4902552 0.4903780 0.4905008
## [1268] 0.4906236 0.4907464 0.4908692 0.4909920 0.4911148 0.4912376 0.4913603
## [1275] 0.4914831 0.4916059 0.4917287 0.4918515 0.4919743 0.4920971 0.4922199
## [1282] 0.4923427 0.4924654 0.4925882 0.4927110 0.4928338 0.4929566 0.4930794
## [1289] 0.4932022 0.4933250 0.4934478 0.4935705 0.4936933 0.4938161 0.4939389
## [1296] 0.4940617 0.4941845 0.4943073 0.4944301 0.4945529 0.4946756 0.4947984
## [1303] 0.4949212 0.4950440 0.4951668 0.4952896 0.4954124 0.4955352 0.4956580
## [1310] 0.4957807 0.4959035 0.4960263 0.4961491 0.4962719 0.4963947 0.4965175
## [1317] 0.4966403 0.4967630 0.4968858 0.4970086 0.4971314 0.4972542 0.4973770
## [1324] 0.4974998 0.4976226 0.4977454 0.4978681 0.4979909 0.4981137 0.4982365
## [1331] 0.4983593 0.4984821 0.4986049 0.4987277 0.4988505 0.4989732 0.4990960
## [1338] 0.4992188 0.4993416 0.4994644 0.4995872 0.4997100 0.4998328 0.4999556
## [1345] 0.5000783 0.5002011 0.5003239 0.5004467 0.5005695 0.5006923 0.5008151
## [1352] 0.5009379 0.5010607 0.5011834 0.5013062 0.5014290 0.5015518 0.5016746
## [1359] 0.5017974 0.5019202 0.5020430 0.5021658 0.5022885 0.5024113 0.5025341
## [1366] 0.5026569 0.5027797 0.5029025 0.5030253 0.5031481 0.5032709 0.5033936
## [1373] 0.5035164 0.5036392 0.5037620 0.5038848 0.5040076 0.5041304 0.5042532
## [1380] 0.5043760 0.5044987 0.5046215 0.5047443 0.5048671 0.5049899 0.5051127
## [1387] 0.5052355 0.5053583 0.5054811 0.5056038 0.5057266 0.5058494 0.5059722
## [1394] 0.5060950 0.5062178 0.5063406 0.5064634 0.5065862 0.5067089 0.5068317
## [1401] 0.5069545 0.5070773 0.5072001 0.5073229 0.5074457 0.5075685 0.5076913
## [1408] 0.5078140 0.5079368 0.5080596 0.5081824 0.5083052 0.5084280 0.5085508
## [1415] 0.5086736 0.5087964 0.5089191 0.5090419 0.5091647 0.5092875 0.5094103
## [1422] 0.5095331 0.5096559 0.5097787 0.5099015 0.5100242 0.5101470 0.5102698
## [1429] 0.5103926 0.5105154 0.5106382 0.5107610 0.5108838 0.5110065 0.5111293
## [1436] 0.5112521 0.5113749 0.5114977 0.5116205 0.5117433 0.5118661 0.5119889
## [1443] 0.5121116 0.5122344 0.5123572 0.5124800 0.5126028 0.5127256 0.5128484
## [1450] 0.5129712 0.5130940 0.5132167 0.5133395 0.5134623 0.5135851 0.5137079
## [1457] 0.5138307 0.5139535 0.5140763 0.5141991 0.5143218
##
##
## $history
## # A tibble: 1,461 × 5
## ds y floor t y_scaled
## <dttm> <dbl> <dbl> <dbl> <dbl>
## 1 2013-01-01 00:00:00 1588 0 0 0.317
## 2 2013-01-02 00:00:00 1538 0 0.000685 0.307
## 3 2013-01-03 00:00:00 1635 0 0.00137 0.327
## 4 2013-01-04 00:00:00 1741 0 0.00205 0.348
## 5 2013-01-05 00:00:00 1887 0 0.00274 0.377
## 6 2013-01-06 00:00:00 1956 0 0.00342 0.391
## 7 2013-01-07 00:00:00 1313 0 0.00411 0.262
## 8 2013-01-08 00:00:00 1538 0 0.00479 0.307
## 9 2013-01-09 00:00:00 1633 0 0.00548 0.326
## 10 2013-01-10 00:00:00 1677 0 0.00616 0.335
## # ℹ 1,451 more rows
##
## $history.dates
## [1] "2013-01-01 GMT" "2013-01-02 GMT" "2013-01-03 GMT" "2013-01-04 GMT"
## [5] "2013-01-05 GMT" "2013-01-06 GMT" "2013-01-07 GMT" "2013-01-08 GMT"
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## [721] "2014-12-22 GMT" "2014-12-23 GMT" "2014-12-24 GMT" "2014-12-25 GMT"
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## [733] "2015-01-03 GMT" "2015-01-04 GMT" "2015-01-05 GMT" "2015-01-06 GMT"
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## [753] "2015-01-23 GMT" "2015-01-24 GMT" "2015-01-25 GMT" "2015-01-26 GMT"
## [757] "2015-01-27 GMT" "2015-01-28 GMT" "2015-01-29 GMT" "2015-01-30 GMT"
## [761] "2015-01-31 GMT" "2015-02-01 GMT" "2015-02-02 GMT" "2015-02-03 GMT"
## [765] "2015-02-04 GMT" "2015-02-05 GMT" "2015-02-06 GMT" "2015-02-07 GMT"
## [769] "2015-02-08 GMT" "2015-02-09 GMT" "2015-02-10 GMT" "2015-02-11 GMT"
## [773] "2015-02-12 GMT" "2015-02-13 GMT" "2015-02-14 GMT" "2015-02-15 GMT"
## [777] "2015-02-16 GMT" "2015-02-17 GMT" "2015-02-18 GMT" "2015-02-19 GMT"
## [781] "2015-02-20 GMT" "2015-02-21 GMT" "2015-02-22 GMT" "2015-02-23 GMT"
## [785] "2015-02-24 GMT" "2015-02-25 GMT" "2015-02-26 GMT" "2015-02-27 GMT"
## [789] "2015-02-28 GMT" "2015-03-01 GMT" "2015-03-02 GMT" "2015-03-03 GMT"
## [793] "2015-03-04 GMT" "2015-03-05 GMT" "2015-03-06 GMT" "2015-03-07 GMT"
## [797] "2015-03-08 GMT" "2015-03-09 GMT" "2015-03-10 GMT" "2015-03-11 GMT"
## [801] "2015-03-12 GMT" "2015-03-13 GMT" "2015-03-14 GMT" "2015-03-15 GMT"
## [805] "2015-03-16 GMT" "2015-03-17 GMT" "2015-03-18 GMT" "2015-03-19 GMT"
## [809] "2015-03-20 GMT" "2015-03-21 GMT" "2015-03-22 GMT" "2015-03-23 GMT"
## [813] "2015-03-24 GMT" "2015-03-25 GMT" "2015-03-26 GMT" "2015-03-27 GMT"
## [817] "2015-03-28 GMT" "2015-03-29 GMT" "2015-03-30 GMT" "2015-03-31 GMT"
## [821] "2015-04-01 GMT" "2015-04-02 GMT" "2015-04-03 GMT" "2015-04-04 GMT"
## [825] "2015-04-05 GMT" "2015-04-06 GMT" "2015-04-07 GMT" "2015-04-08 GMT"
## [829] "2015-04-09 GMT" "2015-04-10 GMT" "2015-04-11 GMT" "2015-04-12 GMT"
## [833] "2015-04-13 GMT" "2015-04-14 GMT" "2015-04-15 GMT" "2015-04-16 GMT"
## [837] "2015-04-17 GMT" "2015-04-18 GMT" "2015-04-19 GMT" "2015-04-20 GMT"
## [841] "2015-04-21 GMT" "2015-04-22 GMT" "2015-04-23 GMT" "2015-04-24 GMT"
## [845] "2015-04-25 GMT" "2015-04-26 GMT" "2015-04-27 GMT" "2015-04-28 GMT"
## [849] "2015-04-29 GMT" "2015-04-30 GMT" "2015-05-01 GMT" "2015-05-02 GMT"
## [853] "2015-05-03 GMT" "2015-05-04 GMT" "2015-05-05 GMT" "2015-05-06 GMT"
## [857] "2015-05-07 GMT" "2015-05-08 GMT" "2015-05-09 GMT" "2015-05-10 GMT"
## [861] "2015-05-11 GMT" "2015-05-12 GMT" "2015-05-13 GMT" "2015-05-14 GMT"
## [865] "2015-05-15 GMT" "2015-05-16 GMT" "2015-05-17 GMT" "2015-05-18 GMT"
## [869] "2015-05-19 GMT" "2015-05-20 GMT" "2015-05-21 GMT" "2015-05-22 GMT"
## [873] "2015-05-23 GMT" "2015-05-24 GMT" "2015-05-25 GMT" "2015-05-26 GMT"
## [877] "2015-05-27 GMT" "2015-05-28 GMT" "2015-05-29 GMT" "2015-05-30 GMT"
## [881] "2015-05-31 GMT" "2015-06-01 GMT" "2015-06-02 GMT" "2015-06-03 GMT"
## [885] "2015-06-04 GMT" "2015-06-05 GMT" "2015-06-06 GMT" "2015-06-07 GMT"
## [889] "2015-06-08 GMT" "2015-06-09 GMT" "2015-06-10 GMT" "2015-06-11 GMT"
## [893] "2015-06-12 GMT" "2015-06-13 GMT" "2015-06-14 GMT" "2015-06-15 GMT"
## [897] "2015-06-16 GMT" "2015-06-17 GMT" "2015-06-18 GMT" "2015-06-19 GMT"
## [901] "2015-06-20 GMT" "2015-06-21 GMT" "2015-06-22 GMT" "2015-06-23 GMT"
## [905] "2015-06-24 GMT" "2015-06-25 GMT" "2015-06-26 GMT" "2015-06-27 GMT"
## [909] "2015-06-28 GMT" "2015-06-29 GMT" "2015-06-30 GMT" "2015-07-01 GMT"
## [913] "2015-07-02 GMT" "2015-07-03 GMT" "2015-07-04 GMT" "2015-07-05 GMT"
## [917] "2015-07-06 GMT" "2015-07-07 GMT" "2015-07-08 GMT" "2015-07-09 GMT"
## [921] "2015-07-10 GMT" "2015-07-11 GMT" "2015-07-12 GMT" "2015-07-13 GMT"
## [925] "2015-07-14 GMT" "2015-07-15 GMT" "2015-07-16 GMT" "2015-07-17 GMT"
## [929] "2015-07-18 GMT" "2015-07-19 GMT" "2015-07-20 GMT" "2015-07-21 GMT"
## [933] "2015-07-22 GMT" "2015-07-23 GMT" "2015-07-24 GMT" "2015-07-25 GMT"
## [937] "2015-07-26 GMT" "2015-07-27 GMT" "2015-07-28 GMT" "2015-07-29 GMT"
## [941] "2015-07-30 GMT" "2015-07-31 GMT" "2015-08-01 GMT" "2015-08-02 GMT"
## [945] "2015-08-03 GMT" "2015-08-04 GMT" "2015-08-05 GMT" "2015-08-06 GMT"
## [949] "2015-08-07 GMT" "2015-08-08 GMT" "2015-08-09 GMT" "2015-08-10 GMT"
## [953] "2015-08-11 GMT" "2015-08-12 GMT" "2015-08-13 GMT" "2015-08-14 GMT"
## [957] "2015-08-15 GMT" "2015-08-16 GMT" "2015-08-17 GMT" "2015-08-18 GMT"
## [961] "2015-08-19 GMT" "2015-08-20 GMT" "2015-08-21 GMT" "2015-08-22 GMT"
## [965] "2015-08-23 GMT" "2015-08-24 GMT" "2015-08-25 GMT" "2015-08-26 GMT"
## [969] "2015-08-27 GMT" "2015-08-28 GMT" "2015-08-29 GMT" "2015-08-30 GMT"
## [973] "2015-08-31 GMT" "2015-09-01 GMT" "2015-09-02 GMT" "2015-09-03 GMT"
## [977] "2015-09-04 GMT" "2015-09-05 GMT" "2015-09-06 GMT" "2015-09-07 GMT"
## [981] "2015-09-08 GMT" "2015-09-09 GMT" "2015-09-10 GMT" "2015-09-11 GMT"
## [985] "2015-09-12 GMT" "2015-09-13 GMT" "2015-09-14 GMT" "2015-09-15 GMT"
## [989] "2015-09-16 GMT" "2015-09-17 GMT" "2015-09-18 GMT" "2015-09-19 GMT"
## [993] "2015-09-20 GMT" "2015-09-21 GMT" "2015-09-22 GMT" "2015-09-23 GMT"
## [997] "2015-09-24 GMT" "2015-09-25 GMT" "2015-09-26 GMT" "2015-09-27 GMT"
## [1001] "2015-09-28 GMT" "2015-09-29 GMT" "2015-09-30 GMT" "2015-10-01 GMT"
## [1005] "2015-10-02 GMT" "2015-10-03 GMT" "2015-10-04 GMT" "2015-10-05 GMT"
## [1009] "2015-10-06 GMT" "2015-10-07 GMT" "2015-10-08 GMT" "2015-10-09 GMT"
## [1013] "2015-10-10 GMT" "2015-10-11 GMT" "2015-10-12 GMT" "2015-10-13 GMT"
## [1017] "2015-10-14 GMT" "2015-10-15 GMT" "2015-10-16 GMT" "2015-10-17 GMT"
## [1021] "2015-10-18 GMT" "2015-10-19 GMT" "2015-10-20 GMT" "2015-10-21 GMT"
## [1025] "2015-10-22 GMT" "2015-10-23 GMT" "2015-10-24 GMT" "2015-10-25 GMT"
## [1029] "2015-10-26 GMT" "2015-10-27 GMT" "2015-10-28 GMT" "2015-10-29 GMT"
## [1033] "2015-10-30 GMT" "2015-10-31 GMT" "2015-11-01 GMT" "2015-11-02 GMT"
## [1037] "2015-11-03 GMT" "2015-11-04 GMT" "2015-11-05 GMT" "2015-11-06 GMT"
## [1041] "2015-11-07 GMT" "2015-11-08 GMT" "2015-11-09 GMT" "2015-11-10 GMT"
## [1045] "2015-11-11 GMT" "2015-11-12 GMT" "2015-11-13 GMT" "2015-11-14 GMT"
## [1049] "2015-11-15 GMT" "2015-11-16 GMT" "2015-11-17 GMT" "2015-11-18 GMT"
## [1053] "2015-11-19 GMT" "2015-11-20 GMT" "2015-11-21 GMT" "2015-11-22 GMT"
## [1057] "2015-11-23 GMT" "2015-11-24 GMT" "2015-11-25 GMT" "2015-11-26 GMT"
## [1061] "2015-11-27 GMT" "2015-11-28 GMT" "2015-11-29 GMT" "2015-11-30 GMT"
## [1065] "2015-12-01 GMT" "2015-12-02 GMT" "2015-12-03 GMT" "2015-12-04 GMT"
## [1069] "2015-12-05 GMT" "2015-12-06 GMT" "2015-12-07 GMT" "2015-12-08 GMT"
## [1073] "2015-12-09 GMT" "2015-12-10 GMT" "2015-12-11 GMT" "2015-12-12 GMT"
## [1077] "2015-12-13 GMT" "2015-12-14 GMT" "2015-12-15 GMT" "2015-12-16 GMT"
## [1081] "2015-12-17 GMT" "2015-12-18 GMT" "2015-12-19 GMT" "2015-12-20 GMT"
## [1085] "2015-12-21 GMT" "2015-12-22 GMT" "2015-12-23 GMT" "2015-12-24 GMT"
## [1089] "2015-12-25 GMT" "2015-12-26 GMT" "2015-12-27 GMT" "2015-12-28 GMT"
## [1093] "2015-12-29 GMT" "2015-12-30 GMT" "2015-12-31 GMT" "2016-01-01 GMT"
## [1097] "2016-01-02 GMT" "2016-01-03 GMT" "2016-01-04 GMT" "2016-01-05 GMT"
## [1101] "2016-01-06 GMT" "2016-01-07 GMT" "2016-01-08 GMT" "2016-01-09 GMT"
## [1105] "2016-01-10 GMT" "2016-01-11 GMT" "2016-01-12 GMT" "2016-01-13 GMT"
## [1109] "2016-01-14 GMT" "2016-01-15 GMT" "2016-01-16 GMT" "2016-01-17 GMT"
## [1113] "2016-01-18 GMT" "2016-01-19 GMT" "2016-01-20 GMT" "2016-01-21 GMT"
## [1117] "2016-01-22 GMT" "2016-01-23 GMT" "2016-01-24 GMT" "2016-01-25 GMT"
## [1121] "2016-01-26 GMT" "2016-01-27 GMT" "2016-01-28 GMT" "2016-01-29 GMT"
## [1125] "2016-01-30 GMT" "2016-01-31 GMT" "2016-02-01 GMT" "2016-02-02 GMT"
## [1129] "2016-02-03 GMT" "2016-02-04 GMT" "2016-02-05 GMT" "2016-02-06 GMT"
## [1133] "2016-02-07 GMT" "2016-02-08 GMT" "2016-02-09 GMT" "2016-02-10 GMT"
## [1137] "2016-02-11 GMT" "2016-02-12 GMT" "2016-02-13 GMT" "2016-02-14 GMT"
## [1141] "2016-02-15 GMT" "2016-02-16 GMT" "2016-02-17 GMT" "2016-02-18 GMT"
## [1145] "2016-02-19 GMT" "2016-02-20 GMT" "2016-02-21 GMT" "2016-02-22 GMT"
## [1149] "2016-02-23 GMT" "2016-02-24 GMT" "2016-02-25 GMT" "2016-02-26 GMT"
## [1153] "2016-02-27 GMT" "2016-02-28 GMT" "2016-02-29 GMT" "2016-03-01 GMT"
## [1157] "2016-03-02 GMT" "2016-03-03 GMT" "2016-03-04 GMT" "2016-03-05 GMT"
## [1161] "2016-03-06 GMT" "2016-03-07 GMT" "2016-03-08 GMT" "2016-03-09 GMT"
## [1165] "2016-03-10 GMT" "2016-03-11 GMT" "2016-03-12 GMT" "2016-03-13 GMT"
## [1169] "2016-03-14 GMT" "2016-03-15 GMT" "2016-03-16 GMT" "2016-03-17 GMT"
## [1173] "2016-03-18 GMT" "2016-03-19 GMT" "2016-03-20 GMT" "2016-03-21 GMT"
## [1177] "2016-03-22 GMT" "2016-03-23 GMT" "2016-03-24 GMT" "2016-03-25 GMT"
## [1181] "2016-03-26 GMT" "2016-03-27 GMT" "2016-03-28 GMT" "2016-03-29 GMT"
## [1185] "2016-03-30 GMT" "2016-03-31 GMT" "2016-04-01 GMT" "2016-04-02 GMT"
## [1189] "2016-04-03 GMT" "2016-04-04 GMT" "2016-04-05 GMT" "2016-04-06 GMT"
## [1193] "2016-04-07 GMT" "2016-04-08 GMT" "2016-04-09 GMT" "2016-04-10 GMT"
## [1197] "2016-04-11 GMT" "2016-04-12 GMT" "2016-04-13 GMT" "2016-04-14 GMT"
## [1201] "2016-04-15 GMT" "2016-04-16 GMT" "2016-04-17 GMT" "2016-04-18 GMT"
## [1205] "2016-04-19 GMT" "2016-04-20 GMT" "2016-04-21 GMT" "2016-04-22 GMT"
## [1209] "2016-04-23 GMT" "2016-04-24 GMT" "2016-04-25 GMT" "2016-04-26 GMT"
## [1213] "2016-04-27 GMT" "2016-04-28 GMT" "2016-04-29 GMT" "2016-04-30 GMT"
## [1217] "2016-05-01 GMT" "2016-05-02 GMT" "2016-05-03 GMT" "2016-05-04 GMT"
## [1221] "2016-05-05 GMT" "2016-05-06 GMT" "2016-05-07 GMT" "2016-05-08 GMT"
## [1225] "2016-05-09 GMT" "2016-05-10 GMT" "2016-05-11 GMT" "2016-05-12 GMT"
## [1229] "2016-05-13 GMT" "2016-05-14 GMT" "2016-05-15 GMT" "2016-05-16 GMT"
## [1233] "2016-05-17 GMT" "2016-05-18 GMT" "2016-05-19 GMT" "2016-05-20 GMT"
## [1237] "2016-05-21 GMT" "2016-05-22 GMT" "2016-05-23 GMT" "2016-05-24 GMT"
## [1241] "2016-05-25 GMT" "2016-05-26 GMT" "2016-05-27 GMT" "2016-05-28 GMT"
## [1245] "2016-05-29 GMT" "2016-05-30 GMT" "2016-05-31 GMT" "2016-06-01 GMT"
## [1249] "2016-06-02 GMT" "2016-06-03 GMT" "2016-06-04 GMT" "2016-06-05 GMT"
## [1253] "2016-06-06 GMT" "2016-06-07 GMT" "2016-06-08 GMT" "2016-06-09 GMT"
## [1257] "2016-06-10 GMT" "2016-06-11 GMT" "2016-06-12 GMT" "2016-06-13 GMT"
## [1261] "2016-06-14 GMT" "2016-06-15 GMT" "2016-06-16 GMT" "2016-06-17 GMT"
## [1265] "2016-06-18 GMT" "2016-06-19 GMT" "2016-06-20 GMT" "2016-06-21 GMT"
## [1269] "2016-06-22 GMT" "2016-06-23 GMT" "2016-06-24 GMT" "2016-06-25 GMT"
## [1273] "2016-06-26 GMT" "2016-06-27 GMT" "2016-06-28 GMT" "2016-06-29 GMT"
## [1277] "2016-06-30 GMT" "2016-07-01 GMT" "2016-07-02 GMT" "2016-07-03 GMT"
## [1281] "2016-07-04 GMT" "2016-07-05 GMT" "2016-07-06 GMT" "2016-07-07 GMT"
## [1285] "2016-07-08 GMT" "2016-07-09 GMT" "2016-07-10 GMT" "2016-07-11 GMT"
## [1289] "2016-07-12 GMT" "2016-07-13 GMT" "2016-07-14 GMT" "2016-07-15 GMT"
## [1293] "2016-07-16 GMT" "2016-07-17 GMT" "2016-07-18 GMT" "2016-07-19 GMT"
## [1297] "2016-07-20 GMT" "2016-07-21 GMT" "2016-07-22 GMT" "2016-07-23 GMT"
## [1301] "2016-07-24 GMT" "2016-07-25 GMT" "2016-07-26 GMT" "2016-07-27 GMT"
## [1305] "2016-07-28 GMT" "2016-07-29 GMT" "2016-07-30 GMT" "2016-07-31 GMT"
## [1309] "2016-08-01 GMT" "2016-08-02 GMT" "2016-08-03 GMT" "2016-08-04 GMT"
## [1313] "2016-08-05 GMT" "2016-08-06 GMT" "2016-08-07 GMT" "2016-08-08 GMT"
## [1317] "2016-08-09 GMT" "2016-08-10 GMT" "2016-08-11 GMT" "2016-08-12 GMT"
## [1321] "2016-08-13 GMT" "2016-08-14 GMT" "2016-08-15 GMT" "2016-08-16 GMT"
## [1325] "2016-08-17 GMT" "2016-08-18 GMT" "2016-08-19 GMT" "2016-08-20 GMT"
## [1329] "2016-08-21 GMT" "2016-08-22 GMT" "2016-08-23 GMT" "2016-08-24 GMT"
## [1333] "2016-08-25 GMT" "2016-08-26 GMT" "2016-08-27 GMT" "2016-08-28 GMT"
## [1337] "2016-08-29 GMT" "2016-08-30 GMT" "2016-08-31 GMT" "2016-09-01 GMT"
## [1341] "2016-09-02 GMT" "2016-09-03 GMT" "2016-09-04 GMT" "2016-09-05 GMT"
## [1345] "2016-09-06 GMT" "2016-09-07 GMT" "2016-09-08 GMT" "2016-09-09 GMT"
## [1349] "2016-09-10 GMT" "2016-09-11 GMT" "2016-09-12 GMT" "2016-09-13 GMT"
## [1353] "2016-09-14 GMT" "2016-09-15 GMT" "2016-09-16 GMT" "2016-09-17 GMT"
## [1357] "2016-09-18 GMT" "2016-09-19 GMT" "2016-09-20 GMT" "2016-09-21 GMT"
## [1361] "2016-09-22 GMT" "2016-09-23 GMT" "2016-09-24 GMT" "2016-09-25 GMT"
## [1365] "2016-09-26 GMT" "2016-09-27 GMT" "2016-09-28 GMT" "2016-09-29 GMT"
## [1369] "2016-09-30 GMT" "2016-10-01 GMT" "2016-10-02 GMT" "2016-10-03 GMT"
## [1373] "2016-10-04 GMT" "2016-10-05 GMT" "2016-10-06 GMT" "2016-10-07 GMT"
## [1377] "2016-10-08 GMT" "2016-10-09 GMT" "2016-10-10 GMT" "2016-10-11 GMT"
## [1381] "2016-10-12 GMT" "2016-10-13 GMT" "2016-10-14 GMT" "2016-10-15 GMT"
## [1385] "2016-10-16 GMT" "2016-10-17 GMT" "2016-10-18 GMT" "2016-10-19 GMT"
## [1389] "2016-10-20 GMT" "2016-10-21 GMT" "2016-10-22 GMT" "2016-10-23 GMT"
## [1393] "2016-10-24 GMT" "2016-10-25 GMT" "2016-10-26 GMT" "2016-10-27 GMT"
## [1397] "2016-10-28 GMT" "2016-10-29 GMT" "2016-10-30 GMT" "2016-10-31 GMT"
## [1401] "2016-11-01 GMT" "2016-11-02 GMT" "2016-11-03 GMT" "2016-11-04 GMT"
## [1405] "2016-11-05 GMT" "2016-11-06 GMT" "2016-11-07 GMT" "2016-11-08 GMT"
## [1409] "2016-11-09 GMT" "2016-11-10 GMT" "2016-11-11 GMT" "2016-11-12 GMT"
## [1413] "2016-11-13 GMT" "2016-11-14 GMT" "2016-11-15 GMT" "2016-11-16 GMT"
## [1417] "2016-11-17 GMT" "2016-11-18 GMT" "2016-11-19 GMT" "2016-11-20 GMT"
## [1421] "2016-11-21 GMT" "2016-11-22 GMT" "2016-11-23 GMT" "2016-11-24 GMT"
## [1425] "2016-11-25 GMT" "2016-11-26 GMT" "2016-11-27 GMT" "2016-11-28 GMT"
## [1429] "2016-11-29 GMT" "2016-11-30 GMT" "2016-12-01 GMT" "2016-12-02 GMT"
## [1433] "2016-12-03 GMT" "2016-12-04 GMT" "2016-12-05 GMT" "2016-12-06 GMT"
## [1437] "2016-12-07 GMT" "2016-12-08 GMT" "2016-12-09 GMT" "2016-12-10 GMT"
## [1441] "2016-12-11 GMT" "2016-12-12 GMT" "2016-12-13 GMT" "2016-12-14 GMT"
## [1445] "2016-12-15 GMT" "2016-12-16 GMT" "2016-12-17 GMT" "2016-12-18 GMT"
## [1449] "2016-12-19 GMT" "2016-12-20 GMT" "2016-12-21 GMT" "2016-12-22 GMT"
## [1453] "2016-12-23 GMT" "2016-12-24 GMT" "2016-12-25 GMT" "2016-12-26 GMT"
## [1457] "2016-12-27 GMT" "2016-12-28 GMT" "2016-12-29 GMT" "2016-12-30 GMT"
## [1461] "2016-12-31 GMT"
##
## $train.holiday.names
## NULL
##
## $train.component.cols
## additive_terms daily weekly yearly multiplicative_terms
## 1 1 0 0 1 0
## 2 1 0 0 1 0
## 3 1 0 0 1 0
## 4 1 0 0 1 0
## 5 1 0 0 1 0
## 6 1 0 0 1 0
## 7 1 0 0 1 0
## 8 1 0 0 1 0
## 9 1 0 0 1 0
## 10 1 0 0 1 0
## 11 1 0 0 1 0
## 12 1 0 0 1 0
## 13 1 0 0 1 0
## 14 1 0 0 1 0
## 15 1 0 0 1 0
## 16 1 0 0 1 0
## 17 1 0 0 1 0
## 18 1 0 0 1 0
## 19 1 0 0 1 0
## 20 1 0 0 1 0
## 21 1 0 1 0 0
## 22 1 0 1 0 0
## 23 1 0 1 0 0
## 24 1 0 1 0 0
## 25 1 0 1 0 0
## 26 1 0 1 0 0
## 27 1 1 0 0 0
## 28 1 1 0 0 0
## 29 1 1 0 0 0
## 30 1 1 0 0 0
## 31 1 1 0 0 0
## 32 1 1 0 0 0
## 33 1 1 0 0 0
## 34 1 1 0 0 0
##
## $component.modes
## $component.modes$additive
## [1] "yearly" "weekly"
## [3] "daily" "additive_terms"
## [5] "extra_regressors_additive" "holidays"
##
## $component.modes$multiplicative
## [1] "multiplicative_terms" "extra_regressors_multiplicative"
##
##
## $fit.kwargs
## list()
##
## attr(,"class")
## [1] "prophet" "list"
Berdasarkan hasil fitting model diatas bisa dijelaslkan bahwa
model_ts sekarang menyimpan informasi data permintaan
harian pada store 03. Sehingga kita bisa gunakan untuk mengekstrak
informasi deret waktu tersebut untuk melakukan perkiraan selama periode
waktu yang bisa ditentukan. Misalnya kita akan memperkiraan permintaan
penjualan untuk 1 tahun kedepan. Utuk melakukan ini kita harus
menyiapkan data frame yang terdiri dari rentang waktu/tanggal mendatang
yang akan diperkirakan. Untungnya dalam prophet() sudah
menyediakan sebuah fungsi make_future_dataframe()
memudahkan kita untuk menyiapkan data tersebut.
range(train_daily_3$ds)
## [1] "2013-01-01" "2016-12-31"
Bisa dilihat bahwa jangka waktu prediksi mulai dari 2013 s/d 2016
Periode prediksi adalah 1 tahun kedepan atau 365 hari
# menyiapkan tanggal utk prediksi
future_ts <- make_future_dataframe(model_ts, periods = 365, freq = "day")
glimpse(future_ts)
## Rows: 1,826
## Columns: 1
## $ ds <dttm> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0…
# visualisasi hasil forecasting
forecast_ts <- predict(model_ts, future_ts)
plot(model_ts, forecast_ts)
Bisa dilihat bahwa, gambar pada grafik yang berwarna biru menunjukkan hasil forecast yang sudah dilakukan. Titik hitam menunjukkan data dari mulai 2013 sampai 2016. Waktu biru yang tidak ada titik adalah perkiraan permintaan untuk 2017
Dengan prophet dimungkinkan kita memvisulisasikan berdasarkan trend, weekly, dan yearly. Default: - daily: sampling hourly, dan frequency 24 - weekly: sampling daily, dan frequency 7 - yearly: sampling daily dan frequency 365
#visualiasi komponen model
prophet_plot_components(model_ts, forecast_ts)
Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:
# forecast berdasarkan seasionality month (bulan)
model_ts_monthly <- prophet(changepoint.prior.scale = 0.05,
yearly.seasonality = FALSE) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 3) %>%
fit.prophet(train_daily_3)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_ts_monthly <- make_future_dataframe(model_ts_monthly, periods = 365)
forecast_ts_monthly <- predict(model_ts_monthly, future_ts_monthly)
prophet_plot_components(model_ts_monthly, forecast_ts_monthly)
Dalam kasus ini kita akan memvisualisasi tren permintaan dari awal tahun 2017 sampai akhir 2017
#visualisasi dari tren awal 2017 sampai akhir 2017
plot(model_ts_monthly, forecast_ts_monthly)
Bisa dilihat bahwa terjadi nya trend peningkatan permintaan yang relatif tinggi dibandingkan tahun sebelumnya
# Menetapkan hari libur mulai dari tahun 2013 sampai 2016, misal libur di hari natal 25 desember atau tahun baru setiap tanggal 31 desember
holiday <-
data.frame(
holiday = "newyeareve",
ds = dmy(c("31-12-2013","31-12-2014", "31-12-2015", "31-12-2016", "31-12-2017")),
lower_window = -5,
upper_window = 0
)
holiday
## holiday ds lower_window upper_window
## 1 newyeareve 2013-12-31 -5 0
## 2 newyeareve 2014-12-31 -5 0
## 3 newyeareve 2015-12-31 -5 0
## 4 newyeareve 2016-12-31 -5 0
## 5 newyeareve 2017-12-31 -5 0
# visualisasi hasil forecast dengan penambahan efek holiday
model_ts_holiday <- prophet(changepoint.prior.scale = 0.05,
holidays = holiday) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>%
fit.prophet(train_daily_3)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_ts_holiday <- make_future_dataframe(model_ts_holiday, periods = 365)
forecast_ts_holiday <- predict(model_ts_holiday, future_ts_holiday)
plot(model_ts_holiday, forecast_ts_holiday)
# melihat trend dan holiday effect dari perkiraan
prophet_plot_components(model_ts_holiday, forecast_ts_holiday)
Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:
forecast_ts %>%
select(ds, trend, weekly, yearly, yhat)
## ds trend weekly yearly yhat
## 1 2013-01-01 1777.267 -218.55228 -843.8701017 1480.175
## 2 2013-01-02 1776.102 -213.16223 -846.1356825 1482.134
## 3 2013-01-03 1774.937 -29.41662 -849.0561370 1661.794
## 4 2013-01-04 1773.772 159.07673 -852.5068489 1845.672
## 5 2013-01-05 1772.607 356.13985 -856.3437163 2037.733
## 6 2013-01-06 1771.442 545.36929 -860.4087772 2221.732
## 7 2013-01-07 1770.277 -599.45476 -864.5359552 1071.616
## 8 2013-01-08 1769.112 -218.55228 -868.5567610 1447.333
## 9 2013-01-09 1767.947 -213.16223 -872.3057870 1447.809
## 10 2013-01-10 1766.782 -29.41662 -875.6258449 1627.069
## 11 2013-01-11 1765.617 159.07673 -878.3726131 1811.651
## 12 2013-01-12 1764.452 356.13985 -880.4186749 2005.503
## 13 2013-01-13 1763.287 545.36929 -881.6568526 2192.329
## 14 2013-01-14 1762.122 -599.45476 -882.0027655 1045.994
## 15 2013-01-15 1760.957 -218.55228 -881.3965617 1426.338
## 16 2013-01-16 1759.792 -213.16223 -879.8038049 1432.156
## 17 2013-01-17 1758.627 -29.41662 -877.2155158 1617.324
## 18 2013-01-18 1757.462 159.07673 -873.6473981 1808.221
## 19 2013-01-19 1756.297 356.13985 -869.1382997 2008.628
## 20 2013-01-20 1755.132 545.36929 -863.7479820 2202.083
## 21 2013-01-21 1753.967 -599.45476 -857.5542877 1062.287
## 22 2013-01-22 1752.802 -218.55228 -850.6498156 1448.929
## 23 2013-01-23 1751.637 -213.16223 -843.1382197 1460.666
## 24 2013-01-24 1750.471 -29.41662 -835.1302606 1651.254
## 25 2013-01-25 1749.306 159.07673 -826.7397413 1846.973
## 26 2013-01-26 1748.141 356.13985 -818.0794581 2051.532
## 27 2013-01-27 1746.976 545.36929 -809.2572965 2248.418
## 28 2013-01-28 1745.811 -599.45476 -800.3725923 1111.314
## 29 2013-01-29 1744.646 -218.55228 -791.5128679 1499.911
## 30 2013-01-30 1743.481 -213.16223 -782.7510414 1512.898
## 31 2013-01-31 1742.316 -29.41662 -774.1431871 1704.086
## 32 2013-02-01 1741.151 159.07673 -765.7269097 1899.831
## 33 2013-02-02 1739.986 356.13985 -757.5203723 2103.935
## 34 2013-02-03 1738.821 545.36929 -749.5219996 2299.998
## 35 2013-02-04 1737.656 -599.45476 -741.7108539 1161.820
## 36 2013-02-05 1736.491 -218.55228 -734.0476629 1549.221
## 37 2013-02-06 1735.326 -213.16223 -726.4764565 1561.017
## 38 2013-02-07 1734.161 -29.41662 -718.9267535 1751.147
## 39 2013-02-08 1732.996 159.07673 -711.3162207 1946.086
## 40 2013-02-09 1731.831 356.13985 -703.5537147 2149.747
## 41 2013-02-10 1730.666 545.36929 -695.5426063 2345.822
## 42 2013-02-11 1729.501 -599.45476 -687.1842773 1208.192
## 43 2013-02-12 1728.336 -218.55228 -678.3816795 1596.732
## 44 2013-02-13 1727.171 -213.16223 -669.0428402 1610.296
## 45 2013-02-14 1726.006 -29.41662 -659.0842057 1802.835
## 46 2013-02-15 1724.841 159.07673 -648.4337167 2000.814
## 47 2013-02-16 1723.676 356.13985 -637.0335213 2208.112
## 48 2013-02-17 1722.511 545.36929 -624.8422410 2408.368
## 49 2013-02-18 1721.346 -599.45476 -611.8367224 1275.384
## 50 2013-02-19 1720.181 -218.55228 -598.0132186 1668.945
## 51 2013-02-20 1719.016 -213.16223 -583.3879687 1687.795
## 52 2013-02-21 1717.850 -29.41662 -567.9971554 1885.767
## 53 2013-02-22 1716.685 159.07673 -551.8962456 2089.196
## 54 2013-02-23 1715.520 356.13985 -535.1587331 2301.831
## 55 2013-02-24 1714.355 545.36929 -517.8743232 2507.180
## 56 2013-02-25 1713.190 -599.45476 -500.1466145 1378.919
## 57 2013-02-26 1712.025 -218.55228 -482.0903481 1776.713
## 58 2013-02-27 1710.860 -213.16223 -463.8283069 1799.200
## 59 2013-02-28 1709.695 -29.41662 -445.4879589 2000.121
## 60 2013-03-01 1708.530 159.07673 -427.1979430 2205.739
## 61 2013-03-02 1707.365 356.13985 -409.0845034 2419.750
## 62 2013-03-03 1706.200 545.36929 -391.2679775 2625.631
## 63 2013-03-04 1705.035 -599.45476 -373.8594398 1497.051
## 64 2013-03-05 1703.870 -218.55228 -356.9576028 1893.690
## 65 2013-03-06 1702.705 -213.16223 -340.6460618 1914.227
## 66 2013-03-07 1701.540 -29.41662 -324.9909677 2112.462
## 67 2013-03-08 1700.375 159.07673 -310.0391919 2314.742
## 68 2013-03-09 1699.210 356.13985 -295.8170377 2524.863
## 69 2013-03-10 1698.045 545.36929 -282.3295346 2726.414
## 70 2013-03-11 1696.880 -599.45476 -269.5603347 1593.195
## 71 2013-03-12 1695.715 -218.55228 -257.4722138 1985.020
## 72 2013-03-13 1694.550 -213.16223 -246.0081622 2000.709
## 73 2013-03-14 1693.385 -29.41662 -235.0930331 2194.205
## 74 2013-03-15 1692.220 159.07673 -224.6357000 2391.991
## 75 2013-03-16 1691.055 356.13985 -214.5316633 2597.993
## 76 2013-03-17 1689.890 545.36929 -204.6660291 2795.923
## 77 2013-03-18 1688.725 -599.45476 -194.9167779 1659.683
## 78 2013-03-19 1687.560 -218.55228 -185.1582296 2049.179
## 79 2013-03-20 1686.395 -213.16223 -175.2646091 2063.298
## 80 2013-03-21 1685.229 -29.41662 -165.1136120 2256.029
## 81 2013-03-22 1684.064 159.07673 -154.5898721 2453.881
## 82 2013-03-23 1682.899 356.13985 -143.5882372 2660.781
## 83 2013-03-24 1681.734 545.36929 -132.0167615 2860.417
## 84 2013-03-25 1680.569 -599.45476 -119.7993373 1726.645
## 85 2013-03-26 1679.404 -218.55228 -106.8778937 2119.304
## 86 2013-03-27 1678.239 -213.16223 -93.2141072 2137.193
## 87 2013-03-28 1677.074 -29.41662 -78.7905803 2334.197
## 88 2013-03-29 1675.909 159.07673 -63.6114599 2536.704
## 89 2013-03-30 1674.744 356.13985 -47.7024841 2748.511
## 90 2013-03-31 1673.579 545.36929 -31.1104604 2953.168
## 91 2013-04-01 1672.414 -599.45476 -13.9021937 1824.387
## 92 2013-04-02 1671.249 -218.55228 3.8371007 2221.864
## 93 2013-04-03 1670.084 -213.16223 22.0058532 2244.258
## 94 2013-04-04 1668.919 -29.41662 40.4886046 2445.321
## 95 2013-04-05 1667.754 159.07673 59.1588111 2651.319
## 96 2013-04-06 1666.589 356.13985 77.8819095 2865.941
## 97 2013-04-07 1665.424 545.36929 96.5185621 3072.642
## 98 2013-04-08 1664.259 -599.45476 114.9279911 1945.062
## 99 2013-04-09 1663.094 -218.55228 132.9713162 2342.843
## 100 2013-04-10 1661.929 -213.16223 150.5148089 2364.611
## 101 2013-04-11 1660.764 -29.41662 167.4329796 2564.110
## 102 2013-04-12 1659.599 159.07673 183.6114214 2767.617
## 103 2013-04-13 1658.434 356.13985 198.9493422 2978.853
## 104 2013-04-14 1657.269 545.36929 213.3617255 3181.330
## 105 2013-04-15 1656.104 -599.45476 226.7810725 2048.760
## 106 2013-04-16 1654.939 -218.55228 239.1586893 2440.875
## 107 2013-04-17 1653.774 -213.16223 250.4654973 2456.407
## 108 2013-04-18 1652.608 -29.41662 260.6923567 2649.214
## 109 2013-04-19 1651.443 159.07673 269.8499068 2845.700
## 110 2013-04-20 1650.278 356.13985 277.9679392 3049.716
## 111 2013-04-21 1649.113 545.36929 285.0943328 3244.907
## 112 2013-04-22 1647.948 -599.45476 291.2935882 2105.117
## 113 2013-04-23 1646.783 -218.55228 296.6450118 2490.206
## 114 2013-04-24 1645.618 -213.16223 301.2406031 2499.027
## 115 2013-04-25 1644.453 -29.41662 305.1827104 2685.549
## 116 2013-04-26 1643.288 159.07673 308.5815181 2876.276
## 117 2013-04-27 1642.123 356.13985 311.5524359 3075.145
## 118 2013-04-28 1640.958 545.36929 314.2134574 3265.871
## 119 2013-04-29 1639.793 -599.45476 316.6825557 2122.351
## 120 2013-04-30 1638.628 -218.55228 319.0751773 2504.481
## 121 2013-05-01 1637.463 -213.16223 321.5018946 2511.133
## 122 2013-05-02 1636.298 -29.41662 324.0662671 2696.278
## 123 2013-05-03 1635.133 159.07673 326.8629546 2886.403
## 124 2013-05-04 1633.968 356.13985 329.9761189 3085.414
## 125 2013-05-05 1632.803 545.36929 333.4781384 3276.980
## 126 2013-05-06 1631.638 -599.45476 337.4286525 2134.942
## 127 2013-05-07 1630.473 -218.55228 341.8739430 2519.124
## 128 2013-05-08 1629.308 -213.16223 346.8466484 2528.322
## 129 2013-05-09 1628.143 -29.41662 352.3658022 2716.422
## 130 2013-05-10 1626.978 159.07673 358.4371732 2909.821
## 131 2013-05-11 1625.813 356.13985 365.0538842 3112.336
## 132 2013-05-12 1624.648 545.36929 372.1972753 3307.544
## 133 2013-05-13 1623.483 -599.45476 379.8379765 2169.196
## 134 2013-05-14 1622.318 -218.55228 387.9371491 2557.032
## 135 2013-05-15 1621.153 -213.16223 396.4478554 2569.768
## 136 2013-05-16 1619.988 -29.41662 405.3165146 2761.217
## 137 2013-05-17 1618.822 159.07673 414.4844027 2957.713
## 138 2013-05-18 1617.657 356.13985 423.8891606 3163.016
## 139 2013-05-19 1616.492 545.36929 433.4662716 3360.658
## 140 2013-05-20 1615.327 -599.45476 443.1504782 2224.353
## 141 2013-05-21 1614.162 -218.55228 452.8771121 2613.817
## 142 2013-05-22 1613.919 -213.16223 462.5833129 2628.670
## 143 2013-05-23 1613.675 -29.41662 472.2091228 2821.798
## 144 2013-05-24 1613.432 159.07673 481.6984435 3019.537
## 145 2013-05-25 1613.188 356.13985 490.9998513 3225.658
## 146 2013-05-26 1612.945 545.36929 500.0672693 3423.711
## 147 2013-05-27 1612.701 -599.45476 508.8605013 2287.437
## 148 2013-05-28 1612.458 -218.55228 517.3456332 2676.581
## 149 2013-05-29 1612.214 -213.16223 525.4953146 2689.877
## 150 2013-05-30 1611.971 -29.41662 533.2889310 2881.173
## 151 2013-05-31 1611.727 159.07673 540.7126815 3076.846
## 152 2013-06-01 1611.484 356.13985 547.7595760 3280.713
## 153 2013-06-02 1611.240 545.36929 554.4293639 3476.369
## 154 2013-06-03 1610.997 -599.45476 560.7284079 2337.600
## 155 2013-06-04 1610.753 -218.55228 566.6695112 2724.200
## 156 2013-06-05 1610.509 -213.16223 572.2717071 2734.949
## 157 2013-06-06 1610.266 -29.41662 577.5600137 2923.739
## 158 2013-06-07 1610.022 159.07673 582.5651565 3116.994
## 159 2013-06-08 1609.779 356.13985 587.3232565 3318.572
## 160 2013-06-09 1609.535 545.36929 591.8754788 3512.110
## 161 2013-06-10 1609.292 -599.45476 596.2676358 2371.435
## 162 2013-06-11 1609.048 -218.55228 600.5497344 2756.376
## 163 2013-06-12 1608.805 -213.16223 604.7754578 2765.748
## 164 2013-06-13 1608.561 -29.41662 609.0015708 2953.476
## 165 2013-06-14 1608.318 159.07673 613.2872366 3146.012
## 166 2013-06-15 1608.074 356.13985 617.6932390 3347.237
## 167 2013-06-16 1607.831 545.36929 622.2810983 3540.811
## 168 2013-06-17 1607.587 -599.45476 627.1120812 2400.574
## 169 2013-06-18 1607.344 -218.55228 632.2461015 2786.367
## 170 2013-06-19 1607.100 -213.16223 637.7405172 2797.008
## 171 2013-06-20 1606.857 -29.41662 643.6488331 2986.419
## 172 2013-06-21 1606.613 159.07673 650.0193237 3181.039
## 173 2013-06-22 1606.370 356.13985 656.8935978 3384.733
## 174 2013-06-23 1606.126 545.36929 664.3051292 3581.130
## 175 2013-06-24 1605.882 -599.45476 672.2777861 2444.035
## 176 2013-06-25 1605.639 -218.55228 680.8243947 2833.241
## 177 2013-06-26 1605.395 -213.16223 689.9453766 2847.508
## 178 2013-06-27 1605.152 -29.41662 699.6275032 3040.693
## 179 2013-06-28 1604.908 159.07673 709.8428108 3239.158
## 180 2013-06-29 1604.665 356.13985 720.5477218 3446.682
## 181 2013-06-30 1604.421 545.36929 731.6824152 3646.803
## 182 2013-07-01 1604.178 -599.45476 743.1704878 2513.223
## 183 2013-07-02 1603.934 -218.55228 754.9189422 2905.631
## 184 2013-07-03 1603.691 -213.16223 766.8185341 2922.677
## 185 2013-07-04 1603.447 -29.41662 778.7445007 3118.105
## 186 2013-07-05 1603.204 159.07673 790.5576876 3318.168
## 187 2013-07-06 1602.960 356.13985 802.1060783 3526.536
## 188 2013-07-07 1602.717 545.36929 813.2267228 3726.643
## 189 2013-07-08 1604.118 -599.45476 823.7480485 2593.741
## 190 2013-07-09 1605.520 -218.55228 833.4925259 2985.790
## 191 2013-07-10 1606.921 -213.16223 842.2796515 3001.368
## 192 2013-07-11 1608.323 -29.41662 849.9291960 3194.165
## 193 2013-07-12 1609.724 159.07673 856.2646596 3390.395
## 194 2013-07-13 1611.126 356.13985 861.1168634 3593.712
## 195 2013-07-14 1612.527 545.36929 864.3276006 3787.554
## 196 2013-07-15 1613.929 -599.45476 865.7532632 2645.557
## 197 2013-07-16 1615.330 -218.55228 865.2683579 3027.376
## 198 2013-07-17 1616.732 -213.16223 862.7688204 3031.668
## 199 2013-07-18 1618.133 -29.41662 858.1750400 3212.221
## 200 2013-07-19 1619.534 159.07673 851.4345087 3395.376
## 201 2013-07-20 1620.936 356.13985 842.5240123 3584.930
## 202 2013-07-21 1622.337 545.36929 831.4512933 3764.488
## 203 2013-07-22 1623.739 -599.45476 818.2561207 2607.870
## 204 2013-07-23 1625.140 -218.55228 803.0107173 2974.929
## 205 2013-07-24 1626.542 -213.16223 785.8195079 2964.529
## 206 2013-07-25 1627.943 -29.41662 766.8181677 3130.675
## 207 2013-07-26 1629.345 159.07673 746.1719679 3299.923
## 208 2013-07-27 1630.746 356.13985 724.0734309 3476.289
## 209 2013-07-28 1632.148 545.36929 700.7393282 3643.586
## 210 2013-07-29 1633.549 -599.45476 676.4070697 2475.831
## 211 2013-07-30 1634.951 -218.55228 651.3305503 2833.059
## 212 2013-07-31 1636.352 -213.16223 625.7755367 2814.295
## 213 2013-08-01 1637.754 -29.41662 600.0146899 2973.682
## 214 2013-08-02 1639.155 159.07673 574.3223318 3137.884
## 215 2013-08-03 1640.557 356.13985 548.9690725 3310.996
## 216 2013-08-04 1641.958 545.36929 524.2164240 3476.874
## 217 2013-08-05 1643.360 -599.45476 500.3115270 2309.546
## 218 2013-08-06 1644.761 -218.55228 477.4821187 2669.021
## 219 2013-08-07 1646.163 -213.16223 455.9318676 2654.262
## 220 2013-08-08 1647.564 -29.41662 435.8361925 2819.314
## 221 2013-08-09 1648.966 159.07673 417.3386752 2990.711
## 222 2013-08-10 1650.367 356.13985 400.5481633 3172.385
## 223 2013-08-11 1651.769 545.36929 385.5366421 3348.004
## 224 2013-08-12 1653.170 -599.45476 372.3379391 2191.383
## 225 2013-08-13 1654.572 -218.55228 360.9473034 2562.296
## 226 2013-08-14 1655.973 -213.16223 351.3218793 2559.463
## 227 2013-08-15 1657.375 -29.41662 343.3820730 2736.670
## 228 2013-08-16 1658.776 159.07673 337.0137879 2920.196
## 229 2013-08-17 1660.178 356.13985 332.0714798 3113.719
## 230 2013-08-18 1661.579 545.36929 328.3819633 3300.660
## 231 2013-08-19 1662.981 -599.45476 325.7488793 2154.604
## 232 2013-08-20 1664.382 -218.55228 323.9577162 2535.117
## 233 2013-08-21 1665.783 -213.16223 322.7812601 2540.732
## 234 2013-08-22 1667.185 -29.41662 321.9853385 2725.084
## 235 2013-08-23 1669.274 159.07673 321.3347113 2915.015
## 236 2013-08-24 1671.362 356.13985 320.5989596 3113.431
## 237 2013-08-25 1673.451 545.36929 319.5582181 3303.708
## 238 2013-08-26 1675.540 -599.45476 318.0086034 2159.423
## 239 2013-08-27 1677.628 -218.55228 315.7671938 2540.173
## 240 2013-08-28 1679.717 -213.16223 312.6764304 2544.561
## 241 2013-08-29 1681.806 -29.41662 308.6078192 2726.327
## 242 2013-08-30 1683.894 159.07673 303.4648366 2911.766
## 243 2013-08-31 1685.983 356.13985 297.1849578 3104.638
## 244 2013-09-01 1688.071 545.36929 289.7407524 3288.511
## 245 2013-09-02 1690.160 -599.45476 281.1400156 2137.175
## 246 2013-09-03 1692.249 -218.55228 271.4249298 2510.451
## 247 2013-09-04 1694.337 -213.16223 260.6702789 2507.175
## 248 2013-09-05 1696.426 -29.41662 248.9807609 2681.320
## 249 2013-09-06 1698.515 159.07673 236.4874738 2859.409
## 250 2013-09-07 1700.603 356.13985 223.3436686 3045.417
## 251 2013-09-08 1702.692 545.36929 209.7198888 3223.111
## 252 2013-09-09 1704.781 -599.45476 195.7986300 2066.454
## 253 2013-09-10 1706.869 -218.55228 181.7686703 2435.416
## 254 2013-09-11 1708.958 -213.16223 167.8192322 2428.945
## 255 2013-09-12 1711.047 -29.41662 154.1341415 2601.094
## 256 2013-09-13 1713.135 159.07673 140.8861523 2778.428
## 257 2013-09-14 1715.224 356.13985 128.2316030 2964.925
## 258 2013-09-15 1717.313 545.36929 116.3055604 3144.317
## 259 2013-09-16 1719.401 -599.45476 105.2175979 1990.494
## 260 2013-09-17 1721.490 -218.55228 95.0483363 2363.316
## 261 2013-09-18 1723.579 -213.16223 85.8468555 2361.593
## 262 2013-09-19 1725.667 -29.41662 77.6290634 2539.210
## 263 2013-09-20 1727.756 159.07673 70.3770796 2722.540
## 264 2013-09-21 1729.845 356.13985 64.0396660 2915.354
## 265 2013-09-22 1731.933 545.36929 58.5337048 3101.166
## 266 2013-09-23 1734.022 -599.45476 53.7466955 1953.644
## 267 2013-09-24 1736.111 -218.55228 49.5402136 2332.428
## 268 2013-09-25 1738.199 -213.16223 45.7542432 2336.121
## 269 2013-09-26 1740.288 -29.41662 42.2122725 2518.413
## 270 2013-09-27 1742.376 159.07673 38.7270145 2705.510
## 271 2013-09-28 1744.465 356.13985 35.1065980 2901.041
## 272 2013-09-29 1746.554 545.36929 31.1610554 3088.414
## 273 2013-09-30 1748.642 -599.45476 26.7089238 1941.226
## 274 2013-10-01 1750.731 -218.55228 21.5837696 2319.092
## 275 2013-10-02 1752.820 -213.16223 15.6404434 2320.628
## 276 2013-10-03 1754.908 -29.41662 8.7608790 2499.583
## 277 2013-10-04 1756.997 159.07673 0.8592559 2682.263
## 278 2013-10-05 1759.086 356.13985 -8.1136378 2872.442
## 279 2013-10-06 1761.174 545.36929 -18.1669883 3053.707
## 280 2013-10-07 1763.263 -599.45476 -29.2676077 1899.871
## 281 2013-10-08 1765.352 -218.55228 -41.3387481 2270.790
## 282 2013-10-09 1767.440 -213.16223 -54.2601449 2265.348
## 283 2013-10-10 1769.529 -29.41662 -67.8693208 2437.573
## 284 2013-10-11 1771.618 159.07673 -81.9641511 2614.060
## 285 2013-10-12 1773.706 356.13985 -96.3066533 2798.869
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## 290 2013-10-17 1784.150 -29.41662 -161.6015022 2358.461
## 291 2013-10-18 1786.238 159.07673 -171.1682680 2539.477
## 292 2013-10-19 1788.327 356.13985 -178.8422250 2730.954
## 293 2013-10-20 1790.416 545.36929 -184.3453285 2916.769
## 294 2013-10-21 1792.504 -599.45476 -187.4320959 1770.947
## 295 2013-10-22 1794.593 -218.55228 -187.8975279 2153.473
## 296 2013-10-23 1796.681 -213.16223 -185.5842965 2163.265
## 297 2013-10-24 1798.770 -29.41662 -180.3889986 2354.294
## 298 2013-10-25 1800.859 159.07673 -172.2672942 2552.998
## 299 2013-10-26 1802.947 356.13985 -161.2377753 2763.179
## 300 2013-10-27 1805.036 545.36929 -147.3844381 2968.351
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## 303 2013-10-30 1811.302 -213.16223 -90.7123481 2272.757
## 304 2013-10-31 1813.391 -29.41662 -67.7136403 2481.590
## 305 2013-11-01 1815.479 159.07673 -43.2723417 2696.614
## 306 2013-11-02 1817.568 356.13985 -17.8315668 2921.206
## 307 2013-11-03 1819.657 545.36929 8.1250629 3138.481
## 308 2013-11-04 1821.745 -599.45476 34.0823238 2021.703
## 309 2013-11-05 1823.834 -218.55228 59.5031979 2430.115
## 310 2013-11-06 1825.923 -213.16223 83.8393661 2461.930
## 311 2013-11-07 1828.011 -29.41662 106.5421522 2670.467
## 312 2013-11-08 1830.100 159.07673 127.0736677 2881.580
## 313 2013-11-09 1832.189 356.13985 144.9179027 3098.576
## 314 2013-11-10 1834.277 545.36929 159.5915046 3304.568
## 315 2013-11-11 1836.366 -599.45476 170.6539952 2172.895
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## 317 2013-11-13 1840.543 -213.16223 180.4535726 2573.164
## 318 2013-11-14 1842.632 -29.41662 178.6035043 2757.149
## 319 2013-11-15 1844.720 159.07673 171.9809685 2941.108
## 320 2013-11-16 1846.809 356.13985 160.4778450 3128.757
## 321 2013-11-17 1848.898 545.36929 144.0665325 3303.663
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## 323 2013-11-19 1853.075 -218.55228 96.8154296 2496.668
## 324 2013-11-20 1855.164 -213.16223 66.3229012 2473.654
## 325 2013-11-21 1857.252 -29.41662 31.6101225 2624.776
## 326 2013-11-22 1859.341 159.07673 -6.9676448 2776.780
## 327 2013-11-23 1861.430 356.13985 -48.9937624 2933.906
## 328 2013-11-24 1863.518 545.36929 -93.9985201 3080.219
## 329 2013-11-25 1865.607 -599.45476 -141.4684913 1890.014
## 330 2013-11-26 1867.696 -218.55228 -190.8567189 2223.617
## 331 2013-11-27 1869.784 -213.16223 -241.5934994 2180.358
## 332 2013-11-28 1871.873 -29.41662 -293.0975145 2314.689
## 333 2013-11-29 1873.962 159.07673 -344.7870572 2453.581
## 334 2013-11-30 1876.050 356.13985 -396.0910985 2601.429
## 335 2013-12-01 1878.139 545.36929 -446.4599468 2742.378
## 336 2013-12-02 1880.228 -599.45476 -495.3752643 1550.727
## 337 2013-12-03 1882.316 -218.55228 -542.3592240 1886.735
## 338 2013-12-04 1884.405 -213.16223 -586.9826125 1849.590
## 339 2013-12-05 1886.494 -29.41662 -628.8717129 1993.535
## 340 2013-12-06 1888.582 159.07673 -667.7138328 2145.275
## 341 2013-12-07 1890.671 356.13985 -703.2613766 2308.879
## 342 2013-12-08 1892.760 545.36929 -735.3343990 2468.124
## 343 2013-12-09 1894.848 -599.45476 -763.8216135 1296.902
## 344 2013-12-10 1896.937 -218.55228 -788.6798665 1655.035
## 345 2013-12-11 1899.025 -213.16223 -809.9321264 1641.261
## 346 2013-12-12 1901.114 -29.41662 -827.6640702 1809.363
## 347 2013-12-13 1903.203 159.07673 -842.0193845 1985.590
## 348 2013-12-14 1905.291 356.13985 -853.1939243 2173.567
## 349 2013-12-15 1907.380 545.36929 -861.4289009 2356.650
## 350 2013-12-16 1909.469 -599.45476 -867.0032873 1208.341
## 351 2013-12-17 1911.557 -218.55228 -870.2256469 1588.109
## 352 2013-12-18 1913.646 -213.16223 -871.4255986 1594.388
## 353 2013-12-19 1915.735 -29.41662 -870.9451377 1780.703
## 354 2013-12-20 1917.823 159.07673 -869.1300271 1973.100
## 355 2013-12-21 1919.912 356.13985 -866.3214695 2175.060
## 356 2013-12-22 1922.001 545.36929 -862.8482552 2369.852
## 357 2013-12-23 1924.089 -599.45476 -859.0195659 1230.945
## 358 2013-12-24 1926.178 -218.55228 -855.1185906 1617.837
## 359 2013-12-25 1928.267 -213.16223 -851.3970873 1629.037
## 360 2013-12-26 1930.355 -29.41662 -848.0709926 1818.198
## 361 2013-12-27 1932.444 159.07673 -845.3171553 2011.533
## 362 2013-12-28 1934.533 356.13985 -843.2712341 2212.731
## 363 2013-12-29 1936.621 545.36929 -842.0267730 2405.294
## 364 2013-12-30 1938.710 -599.45476 -841.6354302 1262.950
## 365 2013-12-31 1940.799 -218.55228 -842.1083139 1645.468
## 366 2014-01-01 1942.887 -213.16223 -843.4183429 1651.636
## 367 2014-01-02 1944.976 -29.41662 -845.5035310 1835.386
## 368 2014-01-03 1947.065 159.07673 -848.2710686 2023.200
## 369 2014-01-04 1949.153 356.13985 -851.6020590 2219.021
## 370 2014-01-05 1951.242 545.36929 -855.3567530 2406.584
## 371 2014-01-06 1953.330 -599.45476 -859.3801165 1259.825
## 372 2014-01-07 1955.419 -218.55228 -863.5075629 1638.689
## 373 2014-01-08 1957.508 -213.16223 -867.5706802 1642.105
## 374 2014-01-09 1959.596 -29.41662 -871.4027922 1824.107
## 375 2014-01-10 1960.962 159.07673 -874.8441989 2010.525
## 376 2014-01-11 1962.328 356.13985 -877.7469579 2206.051
## 377 2014-01-12 1963.694 545.36929 -879.9790847 2394.414
## 378 2014-01-13 1965.060 -599.45476 -881.4280708 1249.507
## 379 2014-01-14 1966.426 -218.55228 -882.0036408 1631.200
## 380 2014-01-15 1967.792 -213.16223 -881.6396945 1638.320
## 381 2014-01-16 1969.158 -29.41662 -880.2954051 1824.776
## 382 2014-01-17 1970.524 159.07673 -877.9554704 2016.975
## 383 2014-01-18 1971.890 356.13985 -874.6295388 2218.730
## 384 2014-01-19 1973.256 545.36929 -870.3508558 2413.605
## 385 2014-01-20 1974.622 -599.45476 -865.1741980 1275.323
## 386 2014-01-21 1975.988 -218.55228 -859.1731823 1663.593
## 387 2014-01-22 1977.354 -213.16223 -852.4370529 1677.085
## 388 2014-01-23 1978.720 -29.41662 -845.0670627 1869.566
## 389 2014-01-24 1980.086 159.07673 -837.1725745 2067.320
## 390 2014-01-25 1981.452 356.13985 -828.8670129 2274.055
## 391 2014-01-26 1982.818 545.36929 -820.2638000 2473.253
## 392 2014-01-27 1984.184 -599.45476 -811.4724023 1338.587
## 393 2014-01-28 1985.550 -218.55228 -802.5946154 1729.733
## 394 2014-01-29 1986.916 -213.16223 -793.7211968 1745.363
## 395 2014-01-30 1988.282 -29.41662 -784.9289482 1939.266
## 396 2014-01-31 1989.648 159.07673 -776.2783321 2137.776
## 397 2014-02-01 1991.014 356.13985 -767.8116880 2344.672
## 398 2014-02-02 1992.380 545.36929 -759.5520935 2543.527
## 399 2014-02-03 1993.746 -599.45476 -751.5028989 1408.118
## 400 2014-02-04 1995.112 -218.55228 -743.6479355 1798.242
## 401 2014-02-05 1996.478 -213.16223 -735.9523841 1812.693
## 402 2014-02-06 1997.844 -29.41662 -728.3642645 2005.393
## 403 2014-02-07 1999.210 159.07673 -720.8164908 2202.800
## 404 2014-02-08 2000.576 356.13985 -713.2294210 2408.816
## 405 2014-02-09 2001.942 545.36929 -705.5138118 2607.127
## 406 2014-02-10 2003.308 -599.45476 -697.5740825 1471.609
## 407 2014-02-11 2004.674 -218.55228 -689.3117790 1862.140
## 408 2014-02-12 2006.040 -213.16223 -680.6291279 1877.578
## 409 2014-02-13 2007.406 -29.41662 -671.4325660 2071.886
## 410 2014-02-14 2008.772 159.07673 -661.6361343 2271.542
## 411 2014-02-15 2010.138 356.13985 -651.1646299 2480.443
## 412 2014-02-16 2011.504 545.36929 -639.9564179 2682.246
## 413 2014-02-17 2012.870 -599.45476 -627.9658162 1550.779
## 414 2014-02-18 2014.236 -218.55228 -615.1649811 1945.848
## 415 2014-02-19 2015.602 -213.16223 -601.5452359 1966.224
## 416 2014-02-20 2016.968 -29.41662 -587.1178029 2165.763
## 417 2014-02-21 2018.334 159.07673 -571.9139167 2370.826
## 418 2014-02-22 2019.700 356.13985 -555.9843183 2585.185
## 419 2014-02-23 2021.066 545.36929 -539.3981439 2792.367
## 420 2014-02-24 2022.432 -599.45476 -522.2412447 1666.065
## 421 2014-02-25 2023.798 -218.55228 -504.6139884 2065.961
## 422 2014-02-26 2024.219 -213.16223 -486.6286089 2089.758
## 423 2014-02-27 2024.640 -29.41662 -468.4061851 2292.147
## 424 2014-02-28 2025.062 159.07673 -450.0733387 2499.395
## 425 2014-03-01 2025.483 356.13985 -431.7587500 2715.194
## 426 2014-03-02 2025.905 545.36929 -413.5895951 2923.014
## 427 2014-03-03 2026.326 -599.45476 -395.6880104 1796.513
## 428 2014-03-04 2026.747 -218.55228 -378.1676885 2195.357
## 429 2014-03-05 2027.169 -213.16223 -361.1307054 2218.206
## 430 2014-03-06 2027.590 -29.41662 -344.6646719 2418.839
## 431 2014-03-07 2028.012 159.07673 -328.8402924 2623.578
## 432 2014-03-08 2028.433 356.13985 -313.7094010 2836.193
## 433 2014-03-09 2028.854 545.36929 -299.3035325 3040.250
## 434 2014-03-10 2029.276 -599.45476 -285.6330682 1909.518
## 435 2014-03-11 2029.697 -218.55228 -272.6869809 2303.788
## 436 2014-03-12 2030.119 -213.16223 -260.4331860 2321.853
## 437 2014-03-13 2030.540 -29.41662 -248.8194868 2517.634
## 438 2014-03-14 2030.961 159.07673 -237.7750873 2717.593
## 439 2014-03-15 2031.383 356.13985 -227.2126280 2925.640
## 440 2014-03-16 2031.804 545.36929 -217.0306865 3125.473
## 441 2014-03-17 2032.226 -599.45476 -207.1166707 1990.984
## 442 2014-03-18 2032.647 -218.55228 -197.3500237 2382.075
## 443 2014-03-19 2033.068 -213.16223 -187.6056487 2397.630
## 444 2014-03-20 2033.490 -29.41662 -177.7574582 2591.646
## 445 2014-03-21 2033.911 159.07673 -167.6819496 2790.636
## 446 2014-03-22 2034.333 356.13985 -157.2617061 2998.541
## 447 2014-03-23 2034.754 545.36929 -146.3887287 3199.065
## 448 2014-03-24 2035.176 -599.45476 -134.9675081 2066.083
## 449 2014-03-25 2035.597 -218.55228 -122.9177529 2459.457
## 450 2014-03-26 2036.018 -213.16223 -110.1767027 2478.009
## 451 2014-03-27 2036.440 -29.41662 -96.7009653 2675.652
## 452 2014-03-28 2036.861 159.07673 -82.4678315 2878.800
## 453 2014-03-29 2037.283 356.13985 -67.4760354 3091.276
## 454 2014-03-30 2037.704 545.36929 -51.7459441 3296.657
## 455 2014-03-31 2038.125 -599.45476 -35.3191773 2168.681
## 456 2014-04-01 2038.547 -218.55228 -18.2576698 2567.067
## 457 2014-04-02 2038.968 -213.16223 -0.6422098 2590.494
## 458 2014-04-03 2039.390 -29.41662 17.4295055 2792.732
## 459 2014-04-04 2039.811 159.07673 35.8452384 3000.063
## 460 2014-04-05 2040.232 356.13985 54.4809375 3216.183
## 461 2014-04-06 2040.654 545.36929 73.2037459 3424.557
## 462 2014-04-07 2041.075 -599.45476 91.8752090 2298.825
## 463 2014-04-08 2041.497 -218.55228 110.3545945 2698.629
## 464 2014-04-09 2041.918 -213.16223 128.5022382 2722.588
## 465 2014-04-10 2042.339 -29.41662 146.1828263 2924.435
## 466 2014-04-11 2042.761 159.07673 163.2685319 3130.436
## 467 2014-04-12 2043.182 356.13985 179.6419270 3344.294
## 468 2014-04-13 2043.604 545.36929 195.1985977 3549.501
## 469 2014-04-14 2044.025 -599.45476 209.8494033 2419.750
## 470 2014-04-15 2044.446 -218.55228 223.5223266 2814.746
## 471 2014-04-16 2044.868 -213.16223 236.1638775 2833.199
## 472 2014-04-17 2045.289 -29.41662 247.7400244 3028.942
## 473 2014-04-18 2045.711 159.07673 258.2366389 3228.354
## 474 2014-04-19 2046.132 356.13985 267.6594566 3435.261
## 475 2014-04-20 2046.553 545.36929 276.0335642 3633.286
## 476 2014-04-21 2046.975 -599.45476 283.4024413 2496.252
## 477 2014-04-22 2047.396 -218.55228 289.8265906 2884.000
## 478 2014-04-23 2047.818 -213.16223 295.3818045 2895.367
## 479 2014-04-24 2048.239 -29.41662 300.1571211 3084.309
## 480 2014-04-25 2048.660 159.07673 304.2525316 3277.320
## 481 2014-04-26 2049.082 356.13985 307.7765035 3478.328
## 482 2014-04-27 2049.503 545.36929 310.8433878 3671.046
## 483 2014-04-28 2049.925 -599.45476 313.5707788 2529.371
## 484 2014-04-29 2050.346 -218.55228 316.0768946 2913.201
## 485 2014-04-30 2050.767 -213.16223 318.4780404 2921.413
## 486 2014-05-01 2051.189 -29.41662 320.8862168 3107.988
## 487 2014-05-02 2051.610 159.07673 323.4069239 3299.424
## 488 2014-05-03 2052.032 356.13985 326.1372080 3499.639
## 489 2014-05-04 2052.453 545.36929 329.1639884 3692.316
## 490 2014-05-05 2052.875 -599.45476 332.5626921 2551.312
## 491 2014-05-06 2053.296 -218.55228 336.3962145 2936.470
## 492 2014-05-07 2053.717 -213.16223 340.7142162 2946.599
## 493 2014-05-08 2054.139 -29.41662 345.5527557 3135.605
## 494 2014-05-09 2054.560 159.07673 350.9342469 3329.901
## 495 2014-05-10 2054.982 356.13985 356.8677274 3533.319
## 496 2014-05-11 2055.403 545.36929 363.3494094 3729.452
## 497 2014-05-12 2055.824 -599.45476 370.3634856 2592.063
## 498 2014-05-13 2056.246 -218.55228 377.8831530 2980.906
## 499 2014-05-14 2056.667 -213.16223 385.8718162 2994.707
## 500 2014-05-15 2057.089 -29.41662 394.2844282 3187.286
## 501 2014-05-16 2057.510 159.07673 403.0689295 3384.985
## 502 2014-05-17 2057.931 356.13985 412.1677401 3591.569
## 503 2014-05-18 2058.353 545.36929 421.5192696 3790.571
## 504 2014-05-19 2058.774 -599.45476 431.0594047 2655.709
## 505 2014-05-20 2059.196 -218.55228 440.7229449 3046.696
## 506 2014-05-21 2059.617 -213.16223 450.4449554 3062.230
## 507 2014-05-22 2060.038 -29.41662 460.1620163 3256.114
## 508 2014-05-23 2060.460 159.07673 469.8133490 3454.680
## 509 2014-05-24 2060.881 356.13985 479.3418081 3661.693
## 510 2014-05-25 2061.303 545.36929 488.6947329 3860.696
## 511 2014-05-26 2061.724 -599.45476 497.8246543 2725.424
## 512 2014-05-27 2062.145 -218.55228 506.6898633 3115.613
## 513 2014-05-28 2062.567 -213.16223 515.2548445 3129.989
## 514 2014-05-29 2062.988 -29.41662 523.4905863 3322.392
## 515 2014-05-30 2063.410 159.07673 531.3747794 3519.191
## 516 2014-05-31 2063.831 356.13985 538.8919170 3724.193
## 517 2014-06-01 2064.252 545.36929 546.0333105 3920.985
## 518 2014-06-02 2064.674 -599.45476 552.7970343 2783.346
## 519 2014-06-03 2065.095 -218.55228 559.1878122 3171.061
## 520 2014-06-04 2065.517 -213.16223 565.2168557 3182.901
## 521 2014-06-05 2065.938 -29.41662 570.9016623 3372.753
## 522 2014-06-06 2066.359 159.07673 576.2657786 3567.032
## 523 2014-06-07 2066.781 356.13985 581.3385311 3769.589
## 524 2014-06-08 2067.202 545.36929 586.1547232 3964.056
## 525 2014-06-09 2067.624 -599.45476 590.7542943 2824.253
## 526 2014-06-10 2068.045 -218.55228 595.1819349 3210.005
## 527 2014-06-11 2068.466 -213.16223 599.4866494 3220.121
## 528 2014-06-12 2068.888 -29.41662 603.7212544 3408.522
## 529 2014-06-13 2069.309 159.07673 607.9418045 3601.658
## 530 2014-06-14 2069.731 356.13985 612.2069327 3803.407
## 531 2014-06-15 2070.152 545.36929 616.5770961 3997.428
## 532 2014-06-16 2070.574 -599.45476 621.1137195 2857.562
## 533 2014-06-17 2070.995 -218.55228 625.8782320 3243.651
## 534 2014-06-18 2071.416 -213.16223 630.9309944 3254.515
## 535 2014-06-19 2071.838 -29.41662 636.3301216 3444.081
## 536 2014-06-20 2072.259 159.07673 642.1302082 3638.796
## 537 2014-06-21 2072.681 356.13985 648.3809690 3842.531
## 538 2014-06-22 2073.102 545.36929 655.1258161 4038.927
## 539 2014-06-23 2073.523 -599.45476 662.4003954 2901.799
## 540 2014-06-24 2073.945 -218.55228 670.2311131 3290.953
## 541 2014-06-25 2074.366 -213.16223 678.6336873 3305.167
## 542 2014-06-26 2074.788 -29.41662 687.6117629 3498.313
## 543 2014-06-27 2075.209 159.07673 697.1556326 3696.771
## 544 2014-06-28 2075.630 356.13985 707.2411076 3904.341
## 545 2014-06-29 2076.052 545.36929 717.8285833 4104.580
## 546 2014-06-30 2076.473 -599.45476 728.8623434 2971.211
## 547 2014-07-01 2076.895 -218.55228 740.2701445 3363.942
## 548 2014-07-02 2077.316 -213.16223 751.9631199 3381.447
## 549 2014-07-03 2077.737 -29.41662 763.8360339 3577.487
## 550 2014-07-04 2078.159 159.07673 775.7679135 3778.333
## 551 2014-07-05 2078.580 356.13985 787.6230743 3987.673
## 552 2014-07-06 2079.002 545.36929 799.2525502 4188.953
## 553 2014-07-07 2079.423 -599.45476 810.4959223 3055.794
## 554 2014-07-08 2079.844 -218.55228 821.1835371 3447.806
## 555 2014-07-09 2080.266 -213.16223 831.1390862 3463.573
## 556 2014-07-10 2080.687 -29.41662 840.1825147 3656.783
## 557 2014-07-11 2081.109 159.07673 848.1332075 3853.648
## 558 2014-07-12 2081.530 356.13985 854.8134001 4057.813
## 559 2014-07-13 2081.951 545.36929 860.0517419 4252.702
## 560 2014-07-14 2082.373 -599.45476 863.6869405 3111.935
## 561 2014-07-15 2082.794 -218.55228 865.5714028 3495.143
## 562 2014-07-16 2083.216 -213.16223 865.5747868 3500.958
## 563 2014-07-17 2083.637 -29.41662 863.5873745 3683.138
## 564 2014-07-18 2084.058 159.07673 859.5231775 3867.988
## 565 2014-07-19 2084.480 356.13985 853.3226872 4059.272
## 566 2014-07-20 2084.901 545.36929 844.9551885 4240.556
## 567 2014-07-21 2085.323 -599.45476 834.4205603 3085.618
## 568 2014-07-22 2085.744 -218.55228 821.7504989 3454.272
## 569 2014-07-23 2086.166 -213.16223 807.0091105 3445.342
## 570 2014-07-24 2086.587 -29.41662 790.2928308 3612.793
## 571 2014-07-25 2087.008 159.07673 771.7296504 3783.145
## 572 2014-07-26 2087.430 356.13985 751.4776346 3960.377
## 573 2014-07-27 2087.851 545.36929 729.7227496 4128.273
## 574 2014-07-28 2088.273 -599.45476 706.6760203 2960.824
## 575 2014-07-29 2088.694 -218.55228 682.5700664 3318.042
## 576 2014-07-30 2089.115 -213.16223 657.6550776 3298.938
## 577 2014-07-31 2089.537 -29.41662 632.1943070 3457.644
## 578 2014-08-01 2089.958 159.07673 606.4591746 3620.824
## 579 2014-08-02 2090.380 356.13985 580.7240873 3792.573
## 580 2014-08-03 2090.801 545.36929 555.2610897 3956.761
## 581 2014-08-04 2091.222 -599.45476 530.3344694 2787.432
## 582 2014-08-05 2091.644 -218.55228 506.1954432 3144.617
## 583 2014-08-06 2092.065 -213.16223 483.0770530 3127.310
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## 772 2015-02-11 2161.241 -213.16223 -691.4129883 2021.995
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## 823 2015-04-03 2175.592 159.07673 12.8747167 3112.873
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## 870 2015-05-20 2189.537 -213.16223 438.2990584 3180.003
## 871 2015-05-21 2189.843 -29.41662 448.0124764 3373.769
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## 1504 2017-02-12 2600.087 545.36929 -678.3816795 3232.405
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## 1507 2017-02-15 2601.931 -213.16223 -648.4337167 2505.664
## 1508 2017-02-16 2602.545 -29.41662 -637.0335213 2701.425
## 1509 2017-02-17 2603.159 159.07673 -624.8422410 2902.724
## 1510 2017-02-18 2603.774 356.13985 -611.8367224 3113.407
## 1511 2017-02-19 2604.388 545.36929 -598.0132186 3317.074
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## 1516 2017-02-24 2607.460 159.07673 -517.8743232 3013.993
## 1517 2017-02-25 2608.075 356.13985 -500.1466145 3229.398
## 1518 2017-02-26 2608.689 545.36929 -482.0903481 3437.298
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## 1520 2017-02-28 2609.918 -218.55228 -445.4879589 2711.208
## 1521 2017-03-01 2610.533 -213.16223 -427.1979430 2735.502
## 1522 2017-03-02 2611.147 -29.41662 -409.0845034 2937.976
## 1523 2017-03-03 2611.761 159.07673 -391.2679775 3144.900
## 1524 2017-03-04 2612.376 356.13985 -373.8594398 3359.986
## 1525 2017-03-05 2612.990 545.36929 -356.9576028 3566.732
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## 1527 2017-03-07 2614.219 -218.55228 -324.9909677 2836.006
## 1528 2017-03-08 2614.834 -213.16223 -310.0391919 2856.962
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## 1539 2017-03-19 2621.592 545.36929 -185.1582296 3747.133
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## 1544 2017-03-24 2624.665 159.07673 -132.0167615 3417.054
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## 1553 2017-04-02 2630.195 545.36929 3.8371007 3944.731
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## 1586 2017-05-05 2650.471 159.07673 333.4781384 3908.356
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## 1592 2017-05-11 2654.158 -29.41662 365.0538842 3755.125
## 1593 2017-05-12 2654.772 159.07673 372.1972753 3951.376
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## 1595 2017-05-14 2656.001 545.36929 387.9371491 4354.637
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## 1599 2017-05-18 2658.459 -29.41662 423.8891606 3818.261
## 1600 2017-05-19 2659.073 159.07673 433.4662716 4016.946
## 1601 2017-05-20 2659.687 356.13985 443.1504782 4224.308
## 1602 2017-05-21 2660.302 545.36929 452.8771121 4423.878
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## 1605 2017-05-24 2662.145 -213.16223 481.6984435 3696.011
## 1606 2017-05-25 2662.760 -29.41662 490.9998513 3889.673
## 1607 2017-05-26 2663.374 159.07673 500.0672693 4087.848
## 1608 2017-05-27 2663.988 356.13985 508.8605013 4294.319
## 1609 2017-05-28 2664.603 545.36929 517.3456332 4492.648
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## 1635 2017-06-23 2680.578 159.07673 664.3051292 4269.290
## 1636 2017-06-24 2681.193 356.13985 672.2777861 4474.940
## 1637 2017-06-25 2681.807 545.36929 680.8243947 4673.331
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## 1641 2017-06-29 2684.265 -29.41662 720.5477218 4140.726
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## 1643 2017-07-01 2685.494 356.13985 743.1704878 4550.134
## 1644 2017-07-02 2686.108 545.36929 754.9189422 4751.726
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## 1647 2017-07-05 2687.951 -213.16223 790.5576876 4030.677
## 1648 2017-07-06 2688.566 -29.41662 802.1060783 4226.585
## 1649 2017-07-07 2689.180 159.07673 813.2267228 4426.814
## 1650 2017-07-08 2689.795 356.13985 823.7480485 4635.013
## 1651 2017-07-09 2690.409 545.36929 833.4925259 4834.601
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## 1660 2017-07-18 2695.939 -218.55228 858.1750400 4100.892
## 1661 2017-07-19 2696.554 -213.16223 851.4345087 4100.156
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## 1663 2017-07-21 2697.782 159.07673 831.4512933 4453.640
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## 1670 2017-07-28 2702.083 159.07673 700.7393282 4327.229
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## 1712 2017-09-08 2727.890 159.07673 209.7198888 3862.016
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## 1718 2017-09-14 2731.576 -29.41662 128.2316030 3595.721
## 1719 2017-09-15 2732.191 159.07673 116.3055604 3772.903
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## 1721 2017-09-17 2733.420 545.36929 95.0483363 4139.167
## 1722 2017-09-18 2734.034 -599.45476 85.8468555 2985.756
## 1723 2017-09-19 2734.649 -218.55228 77.6290634 3359.055
## 1724 2017-09-20 2735.263 -213.16223 70.3770796 3357.808
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## 1726 2017-09-22 2736.492 159.07673 58.5337048 3719.432
## 1727 2017-09-23 2737.106 356.13985 53.7466955 3912.323
## 1728 2017-09-24 2737.721 545.36929 49.5402136 4097.960
## 1729 2017-09-25 2738.335 -599.45476 45.7542432 2949.964
## 1730 2017-09-26 2738.950 -218.55228 42.2122725 3327.939
## 1731 2017-09-27 2739.564 -213.16223 38.7270145 3330.459
## 1732 2017-09-28 2740.178 -29.41662 35.1065980 3511.198
## 1733 2017-09-29 2740.793 159.07673 31.1610554 3696.361
## 1734 2017-09-30 2741.407 356.13985 26.7089238 3889.586
## 1735 2017-10-01 2742.022 545.36929 21.5837696 4074.305
## 1736 2017-10-02 2742.636 -599.45476 15.6404434 2924.152
## 1737 2017-10-03 2743.251 -218.55228 8.7608790 3298.789
## 1738 2017-10-04 2743.865 -213.16223 0.8592559 3296.892
## 1739 2017-10-05 2744.479 -29.41662 -8.1136378 3472.279
## 1740 2017-10-06 2745.094 159.07673 -18.1669883 3651.334
## 1741 2017-10-07 2745.708 356.13985 -29.2676077 3837.910
## 1742 2017-10-08 2746.323 545.36929 -41.3387481 4015.683
## 1743 2017-10-09 2746.937 -599.45476 -54.2601449 2858.552
## 1744 2017-10-10 2747.552 -218.55228 -67.8693208 3226.460
## 1745 2017-10-11 2748.166 -213.16223 -81.9641511 3218.370
## 1746 2017-10-12 2748.781 -29.41662 -96.3066533 3388.387
## 1747 2017-10-13 2749.395 159.07673 -110.6279327 3563.174
## 1748 2017-10-14 2750.009 356.13985 -124.6341826 3746.845
## 1749 2017-10-15 2750.624 545.36929 -138.0136052 3923.309
## 1750 2017-10-16 2751.238 -599.45476 -150.4440953 2766.669
## 1751 2017-10-17 2751.853 -218.55228 -161.6015022 3137.029
## 1752 2017-10-18 2752.467 -213.16223 -171.1682680 3133.467
## 1753 2017-10-19 2753.082 -29.41662 -178.8422250 3310.153
## 1754 2017-10-20 2753.696 159.07673 -184.3453285 3493.757
## 1755 2017-10-21 2754.310 356.13985 -187.4320959 3688.348
## 1756 2017-10-22 2754.925 545.36929 -187.8975279 3877.727
## 1757 2017-10-23 2755.539 -599.45476 -185.5842965 2735.830
## 1758 2017-10-24 2756.154 -218.55228 -180.3889986 3122.542
## 1759 2017-10-25 2756.768 -213.16223 -172.2672942 3136.669
## 1760 2017-10-26 2757.383 -29.41662 -161.2377753 3332.058
## 1761 2017-10-27 2757.997 159.07673 -147.3844381 3535.019
## 1762 2017-10-28 2758.611 356.13985 -130.8576659 3749.224
## 1763 2017-10-29 2759.226 545.36929 -111.8736672 3958.051
## 1764 2017-10-30 2759.840 -599.45476 -90.7123481 2835.003
## 1765 2017-10-31 2760.455 -218.55228 -67.7136403 3239.519
## 1766 2017-11-01 2761.069 -213.16223 -43.2723417 3269.965
## 1767 2017-11-02 2761.684 -29.41662 -17.8315668 3479.765
## 1768 2017-11-03 2762.298 159.07673 8.1250629 3694.830
## 1769 2017-11-04 2762.913 356.13985 34.0823238 3918.465
## 1770 2017-11-05 2763.527 545.36929 59.5031979 4133.729
## 1771 2017-11-06 2764.141 -599.45476 83.8393661 3013.856
## 1772 2017-11-07 2764.756 -218.55228 106.5421522 3418.076
## 1773 2017-11-08 2765.370 -213.16223 127.0736677 3444.612
## 1774 2017-11-09 2765.985 -29.41662 144.9179027 3646.816
## 1775 2017-11-10 2766.599 159.07673 159.5915046 3850.597
## 1776 2017-11-11 2767.214 356.13985 170.6539952 4059.337
## 1777 2017-11-12 2767.828 545.36929 177.7171863 4256.244
## 1778 2017-11-13 2768.442 -599.45476 180.4535726 3114.771
## 1779 2017-11-14 2769.057 -218.55228 178.6035043 3494.438
## 1780 2017-11-15 2769.671 -213.16223 171.9809685 3493.820
## 1781 2017-11-16 2770.286 -29.41662 160.4778450 3666.677
## 1782 2017-11-17 2770.900 159.07673 144.0665325 3839.373
## 1783 2017-11-18 2771.515 356.13985 122.8008841 4015.785
## 1784 2017-11-19 2772.129 545.36929 96.8154296 4179.644
## 1785 2017-11-20 2772.744 -599.45476 66.3229012 3004.942
## 1786 2017-11-21 2773.358 -218.55228 31.6101225 3351.746
## 1787 2017-11-22 2773.972 -213.16223 -6.9676448 3319.172
## 1788 2017-11-23 2774.587 -29.41662 -48.9937624 3461.506
## 1789 2017-11-24 2775.201 159.07673 -93.9985201 3605.609
## 1790 2017-11-25 2775.816 356.13985 -141.4684913 3755.817
## 1791 2017-11-26 2776.430 545.36929 -190.8567189 3896.273
## 1792 2017-11-27 2777.045 -599.45476 -241.5934994 2701.326
## 1793 2017-11-28 2777.659 -218.55228 -293.0975145 3031.339
## 1794 2017-11-29 2778.273 -213.16223 -344.7870572 2985.654
## 1795 2017-11-30 2778.888 -29.41662 -396.0910985 3118.710
## 1796 2017-12-01 2779.502 159.07673 -446.4599468 3257.449
## 1797 2017-12-02 2780.117 356.13985 -495.3752643 3406.211
## 1798 2017-12-03 2780.731 545.36929 -542.3592240 3549.071
## 1799 2017-12-04 2781.346 -599.45476 -586.9826125 2360.238
## 1800 2017-12-05 2781.960 -218.55228 -628.8717129 2699.866
## 1801 2017-12-06 2782.574 -213.16223 -667.7138328 2667.028
## 1802 2017-12-07 2783.189 -29.41662 -703.2613766 2815.841
## 1803 2017-12-08 2783.803 159.07673 -735.3343990 2972.876
## 1804 2017-12-09 2784.418 356.13985 -763.8216135 3142.066
## 1805 2017-12-10 2785.032 545.36929 -788.6798665 3307.051
## 1806 2017-12-11 2785.647 -599.45476 -809.9321264 2141.590
## 1807 2017-12-12 2786.261 -218.55228 -827.6640702 2505.375
## 1808 2017-12-13 2786.876 -213.16223 -842.0193845 2497.024
## 1809 2017-12-14 2787.490 -29.41662 -853.1939243 2670.209
## 1810 2017-12-15 2788.104 159.07673 -861.4289009 2851.082
## 1811 2017-12-16 2788.719 356.13985 -867.0032873 3043.185
## 1812 2017-12-17 2789.333 545.36929 -870.2256469 3229.807
## 1813 2017-12-18 2789.948 -599.45476 -871.4255986 2084.397
## 1814 2017-12-19 2790.562 -218.55228 -870.9451377 2466.395
## 1815 2017-12-20 2791.177 -213.16223 -869.1300271 2474.214
## 1816 2017-12-21 2791.791 -29.41662 -866.3214695 2661.383
## 1817 2017-12-22 2792.405 159.07673 -862.8482552 2853.964
## 1818 2017-12-23 2793.020 356.13985 -859.0195659 3055.470
## 1819 2017-12-24 2793.634 545.36929 -855.1185906 3249.215
## 1820 2017-12-25 2794.249 -599.45476 -851.3970873 2108.727
## 1821 2017-12-26 2794.863 -218.55228 -848.0709926 2493.570
## 1822 2017-12-27 2795.478 -213.16223 -845.3171553 2502.328
## 1823 2017-12-28 2796.092 -29.41662 -843.2712341 2688.734
## 1824 2017-12-29 2796.706 159.07673 -842.0267730 2879.086
## 1825 2017-12-30 2797.321 356.13985 -841.6354302 3077.155
## 1826 2017-12-31 2797.935 545.36929 -842.1083139 3266.526
Ini digunakan untuk melihat trend perkiraan dengan bentuk lain yaitu dengan menambahkan changepoint
plot(model_ts, forecast_ts) +
add_changepoints_to_plot(model_ts, threshold = 0)
Garis merah putus-putus menunjukkan change point dari trend
before_2017 <- daily_demandstore03 %>%
mutate(
year = year(date)
) %>%
filter(year < 2017) %>%
rename(
ds = "date",
y = "demand"
)
after_2017 <- daily_demandstore03 %>%
mutate(
year = year(date)
) %>%
filter(year >= 2017) %>%
rename(
ds = "date",
y = "demand"
)
ggplot(before_2017, aes(x=ds, y=y)) +
geom_point() +
theme_minimal()
# Model sebelum 2017 dan visualisasinya
model_before_2017 <- prophet(yearly.seasonality = TRUE,
changepoint.prior.scale = 0.01) %>%
fit.prophet(before_2017)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_before_2017 <- make_future_dataframe(model_before_2017, periods = 365)
forecaset_before_2017 <- predict(model_before_2017, future_before_2017)
plot(model_before_2017, forecaset_before_2017) +
add_changepoints_to_plot(model_before_2017) +
geom_point(data = after_2017, aes(x = as.POSIXct(ds), y=y), color = "tomato3")
# Melihat transaksi paling banyak dalam satu minggu
forecast_ts %>%
mutate(
weekday = wday(ds, label = TRUE),
weekly = round(weekly, 5)
) %>%
filter(ds <= max(daily_demandstore03$date)) %>%
select(weekday, weekly) %>%
distinct() %>%
arrange(-weekly)
## Warning: There was 1 warning in `filter()`.
## ℹ In argument: `ds <= max(daily_demandstore03$date)`.
## Caused by warning in `check_tzones()`:
## ! 'tzone' attributes are inconsistent
## weekday weekly
## 1 Sun 545.36929
## 2 Sat 356.13985
## 3 Fri 159.07673
## 4 Thu -29.41662
## 5 Wed -213.16223
## 6 Tue -218.55228
## 7 Mon -599.45476
# Visualisasi Model Sebelum Tahun 2017 berdasarkan hari dalam satu minggu
daily_demandstore03 %>%
mutate(
wday = wday(date, label = TRUE)
) %>%
ggplot(aes(x=date, y=demand)) +
geom_point(aes(color=wday))
Berdasarkan visualisasi diatas dapat disumpulan bahwa penjualan tertinggi pada tiap tahun ada pada hari Jumat, Sabtu dan Minggu
Untuk melakukan evaluasi dari model yang sudah disiapkan, maka kita bisa menguji model tersebut pada data testing.
# Menyiapkan data
test <- read.csv("data/test.csv")
glimpse(test)
## Rows: 182,500
## Columns: 4
## $ date <chr> "2017-01-01", "2017-01-02", "2017-01-03", "2017-01-04", "2017-01…
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ item <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ sales <int> 19, 15, 10, 16, 14, 24, 14, 20, 18, 11, 14, 17, 7, 16, 29, 15, 1…
ada 182500 baris dan 4 kolom untuk data testing
# Merubah type data tanggal menjadi date
test %>%
mutate (date = as.Date(date)) %>%
group_by(date) %>%
summarise(
demand=sum(sales)
)
## # A tibble: 365 × 2
## date demand
## <date> <int>
## 1 2017-01-01 23709
## 2 2017-01-02 15772
## 3 2017-01-03 18650
## 4 2017-01-04 18510
## 5 2017-01-05 19895
## 6 2017-01-06 20994
## 7 2017-01-07 22591
## 8 2017-01-08 23700
## 9 2017-01-09 15797
## 10 2017-01-10 18608
## # ℹ 355 more rows
Bisa dilihat bahwa semua data testing ada pada tahun 2017.
Kita akan bandingkan data set Test dengan data set Training utk data sebelum tahun 2018, karena data train hanya sampai akhir 2016
cutoff <- dmy("01-01-2016")
train <- daily_demandstore03 %>%
filter(
date < cutoff
) %>%
rename(
"ds" = date,
"y" = demand
)
test <- daily_demandstore03 %>%
filter(
date >= cutoff
) %>%
rename(
"ds" = date,
"y" = demand
)
ggplot(daily_demandstore03, aes(x=date, y=demand)) +
geom_point(data = train, aes(x=ds, y=y)) +
geom_point(data = test, aes(x=ds, y=y), color="tomato3")
Warna hitam adalah data training dan warna merah adalah data testing
Model final digunakan untuk mempredisi data testing
# Menyiapkan model final
model_final <- prophet(changepoint.prior.scale = 0.05,
yearly.seasonality = TRUE,
holidays = holiday) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>%
fit.prophet(train)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_final <- make_future_dataframe(model_final, periods = nrow(test) + 1)
forecast_final <- predict(model_final, future_final)
plot(model_final, forecast_final)
plot(model_final, forecast_final) +
geom_point(data = test %>%
mutate(ds = as.POSIXct(ds)), aes(x=ds, y=y), color="tomato3")
Bisa dilihat bahwa model dapat memprediksi data testing dan sama dengan trend yang sudah diperkirakan sebelumnya.
Untuk menentukan tingkat akurasi model, biasanya menghitung terlebih dulu nilai MAPE dari model. MAPE adalah Mean Absolute Persentase Error biasanya digunakan mengavaluasi model deret waktu.
eval <- test %>%
mutate(
ds = as.POSIXct(ds)
) %>%
left_join(forecast_final) %>%
select(ds, y, yhat, yhat_upper, yhat_lower)
## Joining with `by = join_by(ds)`
eval
## # A tibble: 366 × 5
## ds y yhat yhat_upper yhat_lower
## <dttm> <int> <dbl> <dbl> <dbl>
## 1 2016-01-01 00:00:00 2284 2416. 2571. 2253.
## 2 2016-01-02 00:00:00 2384 2616. 2778. 2455.
## 3 2016-01-03 00:00:00 2590 2795. 2955. 2636.
## 4 2016-01-04 00:00:00 1714 1685. 1843. 1526.
## 5 2016-01-05 00:00:00 2004 2046. 2200. 1885.
## 6 2016-01-06 00:00:00 2060 2044. 2203. 1891.
## 7 2016-01-07 00:00:00 2168 2224. 2384. 2056.
## 8 2016-01-08 00:00:00 2343 2398. 2561. 2249.
## 9 2016-01-09 00:00:00 2443 2590. 2749. 2427.
## 10 2016-01-10 00:00:00 2618 2765. 2928. 2604.
## # ℹ 356 more rows
Untuk mendapatkan nilai mape kita harus mengurangi nilai sebenarnya
dengan nilai yang ada pada data testing (yhat) yang ada dalam data frame
forecast_final
mape <- function(y, yhat) {
return(mean(abs(y - yhat)/ y))
}
mape(eval$y, eval$yhat)
## [1] 0.0441405
Bisa dilihat bahwa nilai MAPE dari model adalah 0.04, sehingga akurasi dari model adalah 0,96 (96%). Jadi bisa disimpulkan bahwa model sangat akurat dalam melakukan prediksi.